Shortly before 2 p.m. last Dec. 17, Rep. Claudine Schneider received an urgent telephone call asking her to attend a meeting in the Capitol with Treasury Secretary James A. Baker III.

"When?" the Rhode Island Republican asked.

"In 10 minutes," the Baker aide replied.

The House Ways and Means Committee's tax revision bill was near defeat on the House floor, and the House Republican leadership unanimously opposed it. So Baker, using the office of House Minority Leader Robert H. Michel (R-Ill.), called a meeting of White House allies to try to bypass his own party's leadership.

Gathered for the meeting were nine members of Congress whom Baker knew well and who could be counted on to get the votes of particular blocs. Schneider, for example, was selected because she is a vote-getter in the Northeast, where GOP opposition to the tax bill had been strong.

Baker also selected ranking members of committees and influential senior members, such as William S. Broomfield (R-Mich.) and Henry J. Hyde (R-Ill.). And he drafted the few Republicans from the Ways and Means Committee who supported the bill to have their technical expertise.

After dividing up the lobbying chores, Baker began making personal appeals, negotiating compromises on the bill's fine points and calling on legislators' loyalty to the president.

Later that night, a smiling Baker watched from the visitors' gallery as 49 Republicans joined 207 Democrats to defeat a motion to kill the legislation, 256 to 171. The measure then passed on a voice vote.

After a slow start in his first year as Treasury secretary, Baker has won some of the Reagan administration's toughest political battles. Those include maneuvering the tax bill through a Republican minefield; holding back -- at least temporarily -- congressional protectionist pressures; and proposing the so-called "Baker Plan" for handling the international-debt crisis by increasing loans to hard-pressed nations while requiring them to adopt free-market policies.

For Baker, however, his second year in the Cabinet may prove to be tougher.

Some of this year's problems may be compounded by last year's compromises. In the tax area, for example, Baker won support for what essentially was a Democratic bill by promising a Reagan veto if certain changes were not made in the Republican-controlled Senate. But the Senate Finance Committee, which takes up tax overhaul in March, does not consider itself bound by those promises.

With a record trade deficit in 1985 and a congressional election campaign beginning in the spring, Reagan administration officials say they expect protectionism to become an increasingly hot issue. As the president's chief economic spokesman, Baker has led in devising solutions to the trade problem.

The continuing drop in world oil prices further complicates the international economic outlook and threatens the stability of many Third World countries that depend on oil revenue to survive. It also jeopardizes the Baker Plan, which already has been criticized for being too little, too late.

One high-ranking administration official recently said the Baker Plan would need to be modified because of the oil-price drop. The oil-exporting debtor countries would need to enforce even tougher austerity measures, which the Baker Plan was designed to ease; only then can those debtors improve economically or expect to get more bank financing, the official said.

So far, the administration has come up with no new solution, the official said.

If there has been a theme to Baker's first year at the Treasury Department, it is compromise, analysts within and outside the administration agree.

Soft-spoken and low-key, Baker, 55, works hard to stay out of the limelight. While some cabinet officials are eating pheasant at glittery affairs in Washington, Baker is hunched in a blind on his San Antonio ranch hunting quail. During the high-tension December days when the tax bill was in jeopardy, he and his deputy, Richard G. Darman, spoke to no one as they walked through the halls of the Capitol, followed by a small army of reporters and camera crews.

In a recent interview, Baker declined to accept credit when asked about the House turnaround on the tax bill. "I don't think I did that," he said. "The president did that.

"I worked on the phone," he added. "So did a whole lot of other people."

Repeatedly last year, and in the previous four years when he served as White House chief of staff, Baker was called on by the White House during difficult times. Colleagues and combatants openly admire the skills of the intensely political Houston lawyer/banker, who is known for his smooth-talking, calculated manner, his policy of never going out on a limb and his attention to detail.

Baker collects political chits by attending fundraisers and other political events on behalf of congressional Republicans. His aides note that such actions helped achieve the House tax victory. They added that his contacts could aid Baker in pushing tax overhaul through a nervous Senate.

"He has helped a lot of us," Sen. Charles Grassley (R-Iowa) said. "He was the drawing card at a fundraiser for me last fall."

Commerce Secretary Malcolm Baldrige, who worked with Baker on George Bush's unsuccessful presidential campaign in 1980, said the treasury secretary does not take extreme positions when he finds himself alone on an issue. "Jim Baker is a very practical man," Baldrige said. "He has an open mind. That means to me there's more than one way to skin a cat. It doesn't always have to be done just his way."

Baker's combination of savvy and muted ideology played a large role in last year's turnaround in the administration's policy toward international trade and debt issues.

High-ranking administration officials said Baker showed little or no interest in trade policy before last summer, despite pressure from the Commerce Department and the U.S. Trade Representative's office to deal with the issue at the White House level. When it became clear that trade was fast becoming a dangerous political issue for the president, administration officials said, Baker developed a sudden interest in devising a plan to douse protectionist fires.

In a matter of weeks last summer, the treasury secretary and his deputies devised a plan within the Economic Policy Council, which Baker heads.

From the start, it was clear that any serious effort to deflect protectionism would have to involve lowering the value of the dollar in relation to other currencies. The strong dollar was making U.S. exports expensive overseas. The White House, however, opposed tinkering with foreign exchange markets.

Warning of the need to head off rising protectionist sentiment in Congress, Baker managed to convince the White House to make a 180-degree change in policy.

On Sept. 22, Baker announced an agreement with France, West Germany, Britain and Japan to coordinate efforts to push down the dollar. Since then, the value of the dollar has fallen about 13 percent against other major currencies.

Several high-ranking administration officials credit Baker for helping to move stalled trade-policy initiatives advocated for months by Commerce and the U.S. trade representative. And they credit his influence in the decision to have Reagan make a major trade policy speech and to initiate unfair trading-practice complaints against some countries. The result: Legislation to impose a surcharge on imports languished in committee, and Congress made no attempt to override Reagan's veto of a bill to curb imports of textiles.

"There was a real push given . . . because of rising protectionist sentiment in Congress," Baldrige said in an interview. "That's something Baker really understood. That was true of a great many in the administration who hadn't been closely involved in trade before. What should have been done for their own sake was done because of the rising protectionist sentiment in Congress."

When they devised the monetary plan, officials acknowledged, they knew it wouldn't be enough to change the world. But they also were certain it would deflect some criticism. This spring, Baker will have to come up with something else to quiet Congress, administration officials warn.

Baker also will have to produce a more convincing plan to settle another international problem: the Third World debt crisis. Late last summer, government officials from several Latin American countries complained to Baker that they were struggling under the burden of mounting debt and poor economic growth, and that their debt troubles threatened the stability of their fragile democracies.

With that problem in mind last fall, Baker proposed that commercial banks lend $20 billion to the 15 largest developing-country debtors during the next three years to help ease their problems in repaying loans to western banks. Multilateral development banks would add another $9 billion.

But criticism of the plan is mounting. Late last month, Mexico's finance minister, Jesus Silva Herzog, claimed that the Baker Plan was not enough to restore these 15 countries to economic health. Baker responds that his plan wasn't expected to work overnight and that the complainers also should take steps to help themselves.

"I happen to believe . . . that it's important that the United States lead in international economics," Baker said in an interview. "We should lead where appropriate."

Other administration officials said that the Mexicans, for example, will need to tighten their belts. But, because of falling oil prices, the administration doesn't know what it can do to help Mexico, an official said.

"Some people think the proper course is to write down that debt or write it off and not think in terms of additional capital flows," Baker said. "I think that would not be an alternative approach, but an admission of defeat."

Defeat remains a possibility for Baker on tax overhaul. He frequently reminds visitors that "no one ever said tax reform was going to be easy" and that the Senate is faced not only with restoring deductions and credits dear to senators, but in living up to the promises Reagan has made to change the bill.

The promises, negotiated in part by Baker, helped reassure not only House Republicans but the president himself. In Cabinet meetings, Baker pushed for a quick presidential endorsement of the House bill as soon as it emerged from the Ways and Means Committee in late November, but other aides successfully urged that the president endorse only the general concept of tax overhaul because of substantive objections to the House bill.

The delay and the weak endorsement nearly killed the legislation, giving 164 Republicans political leeway to vote against bringing the bill to the floor. Only then was Baker's advice accepted and the intensive lobbying effort begun.

The promises, outlined in letters to Michel and Rep. Jack Kemp (R-N.Y.), included: a personal exemption of $2,000 for most taxpayers (the House bill would grant the full increase only to those who do not itemize); depreciation write-offs for business investment at least as generous as originally proposed by Reagan; and a top rate of 35 percent (the House bill would cut the current top rate of 50 percent to 38 percent).

These changes would cut federal revenue needed to keep the legislation from adding to the federal deficit.

Baker, who accompanied members of the Senate Finance Committee to their tax "retreat" in West Virginia last month, suggests that the panel look at such revenue-raising proposals as repealing the deduction for state and local taxes. The House ignored that provision of the Reagan plan, and the Senate seems likely to accept only a partial limitation of the deduction, at most.

In his legislative battles, Baker has been criticized by conservatives as not being ideological enough. Critics charge that Baker's compromising has helped give away too much, particularly regarding the agenda begun in the president's first term. Instead, they say, he should fight Congress on principle.

Many of these critics were appointed to Treasury posts during Reagan's first term, when the department was the ideological locus of true-thinking supply-siders and strict monetarists, such as Norman Ture and Paul Craig Roberts.

Administration colleagues say many of the inflexible economic views of the first-term Treasury are gone, making it easier to discuss policy with Treasury subordinates. They point to the resignations of Roberts and Ture, and the departure of Treasury Undersecretary Beryl Sprinkel for the chairmanship of the Council of Economic Advisers.

Although Donald T. Regan has been White House chief of staff for a year and most of his appointees have left Treasury, comparisons continue between Baker and him both in style and substance.

Where Regan would charge ahead on issues regardless of the political costs, Baker contemplates the consequences before deciding an issue's merits, top Treasury aides said.

Baker's low-key style with Congress also sets him apart from Regan. Regan enjoyed sparring at congressional hearings, even when confrontation with angry legislators was expected. Baker, by contrast, is deferential at hearings; he avoids conflict and prefers small meetings and backroom maneuvering, close aides said.

"He sees public hearings as more symbol than substance," a Treasury official said.

"I think there was some damage done when Donald Regan was secretary," said Sen. David H. Pryor (D-Ark). "I think that if the president wants a tax bill, he ought to utilize Jim Baker. He is trusted by the committee. He's practical. He listens. He's open-minded."

"The bottom line is: too much politics and not enough economics," said economist John Makin of the American Enterprise Institute regarding the changes Baker made and accepted in the tax plan. But Makin agreed that Baker would have been "dealt out of the game" if he had resisted the tax legislation on ideological grounds.

Economist Alan Greenspan, who has observed Treasury secretaries during the past two decades, said Baker has the potential to follow in the footsteps of such great secretaries as George Shultz, currently secretary of State, and Robert Anderson, who served during the Eisenhower administration.

However, the challenges of Baker's second year -- taxes, trade and debt -- are tougher than those faced by his predecessors, Greenspan said.

"He's in a period when international financial problems and other areas in which the Treasury functions have become critical," Greenspan said. "At this point, he has at least attained the status of average, and could very well, depending on how the rest of the term transpires, become one of the best."