An election year is dawning. Republican hopes are pinned to prospects for a trouble-free economy. But with the dollar skidding to historic lows at the end of 1987, the new year is starting off on a worrisome note for the man on whom the GOP is depending -- Treasury Secretary James A. Baker III.

The dollar's latest dive came despite a flurry of moves by Baker aimed at restoring financial confidence. The week before Christmas, the Treasury secretary wrapped up negotiations on legislation to curb the budget deficit, then promptly announced an agreement promising economic coordination among seven major industrial nations. The following week, the Treasury and the Mexican government announced a plan to reduce Mexico's debt burden.

Characteristically for a Texas lawyer with a keen sense of political constraints, Baker cut deals that make incremental progress towardsolving the economy's problems. Now, administration officials are crossing their fingers that incremental progress will be enough to calm financial markets and prevent a surge in interest rates and unemployment this year.

No one appreciates the political stakes more than Baker, a former campaign manager for Vice President George Bush. A healthy economy could translate into a big win for Republicans, who claim two strong presidential candidates -- Bush and Sen. Robert J. Dole of Kansas. At the same time, a rise in joblessness, or even a new crisis on Wall Street, could induce voters to back Democrats on the theory that a Republican administration has mismanaged economic policy.

Baker is counting on a number of things going right, including a bottoming-out of the dollar and an improvement in the trade deficit. One potential danger -- default by a big Third World debtor -- appears to have abated for now. The announcement of the Mexican debt plan has quieted fears that Argentina or Brazil will soon repudiate their obligations, because the plan appears to offer new hope to debtors that straighten out their economies.

But the budget and trade deficits "remain serious," and on those fronts, "such changes as there are, are only marginal," said Frederick N. Khedouri, a former Reagan administration budget official.

The financial markets probably recognize the necessity of waiting for a new administration to take more substantive measures to shrink the twin deficits, said Khedouri, an investment banker at Bear, Stearns & Co. "At this stage in the American election cycle, it's impossible for Baker to do much more," he said. But if the markets conclude that prompt action is required, he added, "then we're in trouble."

Behind Baker's strategy is the expectation that the markets will find grounds for remaining patient.

One of the things the Treasury secretary is banking on, according to administration officials, is that the monthly trade figures will finally begin to improve in response to the cheaper dollar. A lower dollar makes American goods more competitive on world markets, but so far the trade gap has failed to narrow. This has been a major cause of Wall Street's pessimism, because analysts fear that foreign investors are growing reluctant to continue pouring money into the U.S. economy.

Many economists predict that the trade deficit will recede a bit this year, but they also say it has become increasingly clear that a cheap dollar won't accomplish enough. They argue that the budget deficit must be slashed in order to diminish America's excessive demand for imported goods. They argue that exporting powerhouses like West Germany must spur domestic growth to absorb more products from other nations.

Baker agrees with this logic, and administration officials are hoping that the markets will appreciate the modest gains that have been made toward those goals.

The fact that the administration and Congress were able to enact any budget legislation at all "means that the markets aren't seeing everybody at loggerheads and in total stalemate," one official said. And the accord among the Group of Seven industrial countries followed significant progress by Japan in stimulating its economy and more limited steps by Bonn, officials note.

But analysts have generally derided the budget and G-7 deals as little more than symbolic exercises that paper over significant differences between the White House and Congress, and between the United States and its trading partners. The budget legislation will only keep the federal government's red ink from rising much above the 1987 level, and the two major parties remain deeply divided over spending and taxes.

The G-7 accord, meanwhile, contains no new pledges for governments to change their policies, only a vague assertion that "a further decline of the dollar ... could be counterproductive."

Given the absence of more substantive policy actions, the dollar is likely to continue falling despite the G-7's proclamations that it shouldn't, in the view of many experts.

Baker worries about a plunge in the U.S. currency, officials say, because he fears it could trigger a panic in financial markets. But the only thing that may prevent a plunge is a rise in U.S. interest rates, which would boost the greenback by making dollar-denominated investments more attractive.

"We will need higher interest rates -- or we're going to get a lower dollar," said Klaus Friedrich, a former Federal Reserve official. Echoing a widely held view, Friedrich said: "We're working up to getting one or the other."

Baker badly wants to avoid a rise in interest rates this year, and so far he has rejected European demands that the United States promise publicly to defend the dollar with higher rates.

His position reflects a growing belief, both inside the administration and the Federal Reserve, that the dollar is reaching bottom, officials say.

It also reflects the administration's belief that U.S. economic growth is slowing down. A softening economy couldn't sustain higher interest costs for long, so Baker sees no point in promising to lift rates.

Indeed, administration officials sound as if they welcome the prospect of relatively slow growth this year, because it involves the least danger of economic chaos.

Administration economists observe that a number of private forecasters have been predicting disaster for the economy, albeit for disparate reasons.

One group is warning that the economy is headed for recession because the Oct. 19 stock market collapse wrecked consumer confidence.

Another fears that the market's woes won't slow consumer spending much at all, and that the economy will overheat as U.S. companies find themselves unable to satisfy the boom in demand for their products abroad and at home. Adherents of this school warn that an overheated economy could rekindle inflation and send interest rates soaring.

"If we fall in between {the two scenarios}, it will be a pretty good year," said one official. "I think there's a reasonable shot." But he added: "It is a time of more uncertainty than usual."