President Reagan's fiscal 1986 budget got off to a faltering start in Congress yesterday as Democrats pounced on proposals to cut programs for middle-class voters and Republicans offered little more than lukewarm support for the plan as a whole.

However, prospects for quick development of a congressional alternative to the president's plan appeared shaky.

The Democrats seized on the president's proposals for cuts in middle-class programs, such as student loans, farm supports and veterans benefits.

"I urge the president to take the time to educate the country on his various budget proposals and to tell people how they will be affected," said House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass). Starting this weekend, the House Budget Committee plans to hold a series of regional hearings around the country to "aid in this education effort."

Meanwhile, Senate Majority Leader Robert J. Dole (R-Kan.), who said a month ago that Senate Republicans would have an alternative plan for deficit reductions by Feb. 1, indicated yesterday that the Senate Budget Committee would take over the job of drafting the plan, which is expected to take five or six weeks.

While there is strong sentiment in the Senate's GOP majority for substantial deficit reductions, the senators have been unable to agree on specific domestic spending cuts or on how extensively to cut the administration's military buildup.

Despite the criticism of Reagan's budget, which for the fifth year in a row proposes massive shifts of money from domestic to defense programs, there was general agreement that he will get at least some of the domestic-spending cuts he seeks and possibly half of the defense growth he requested.

But the clear message was that the first budget of Reagan's second term did not land on the greased skids that four years ago awaited the first budget of his first term.

Not only was there a chilly reaction from many lawmakers, but powerful constituencies for many of the threatened programs, including cities faced with the loss of revenue-sharing, lost no time in marshaling for a fight.

"It's going to be very difficult to do many of the things the president sets forth in his budget," Dole said.

House Minority Leader Robert H. Michel (R-Ill.) described Reagan's budget proposal as a "starting point" but added, "I do not endorse every recommendation in the budget message."

Some Republicans, especially moderates and first-term senators who are up for reelection in 1986, were more sharply critical.

Senate Appropriations Committee Chairman Mark O. Hatfield (R-Ore.) was among the most acerbic of the budget's critics, calling it a "fantasy budget conceived in the land of never-ending deficits."

Sen. James Abdnor (R-S.D.), a strong Reagan supporter who is up for reelection in two years, was nearly as heated in his reaction, especially to proposals for rollbacks in farm subsidies. Calling the budget proposal "unfair to rural America," he said, "A proposed 13 percent defense increase and a drastic farm and rural decrease is unthinkable; I'm against it."

Among Democrats, including some who have been among the staunchest critics of previous Reagan budgets, there was no rush to proclaim this budget to be "dead on arrival," as there was in the last couple of years.

The reason was that the Democrats, who have had trouble with middle-class voters, sense an opportunity to win favor with that group by defending many of the middle-class programs that Reagan would cut.

Hence they want to keep Reagan's budget alive long enough -- on life-support systems, if necessary -- to exploit it politically. The Democrats similarly painted themselves as defenders of the poor when Reagan, in his previous budgets, concentrated his domestic-spending cuts on programs aimed at the less affluent.

"The administration budget released today sends a tough message to the American middle class . . . . It takes the pain of budget cutting directly to middle America," O'Neill said in a statement that otherwise maintained the conciliatory tone of his post-election comments on Reagan.

House Budget Commitee member Vic Fazio (D-Calif.) spelled out the Democratic strategy even more clearly. In the past, Reagan has sent up a budget proposal with such an "outlandish set of numbers" that it was declared "dead on arrival by members of his own party and then [Reagan would] go around the country blaming Congress." This year, Fazio said, the Budget Committee "intends to give the American people an opportunity to examine the president's choices and their impact."

The congressional jockeying for position on the budget came as Reagan and his budget director, David A. Stockman, stepped up their rhetorical pressure for enactment of its key provisions.

"We can't wait a moment longer to get our federal budget under control," said Reagan at a White House briefing for congressional leaders. "If we lose the budget battle," he added, "if we allow all the lessons of all the decades of unchecked government spending to go unheeded, we consign ourselves and our children to the tyranny of a government that respects no boundaries and knows no limits."

He held out a hint of compromise, which Senate Republicans have said is essential to passage of deficit reductions sufficient to meet their goal of cutting deficits by half to $100 billion a year in three years, a goal once shared by the White House but abandoned in the budget submitted yesterday. But the president defended his defense buildup and refusal to consider tax increases.

Stockman spoke in a similar vein, saying, "The day of reckoning has arrived . . . . The hour is almost too late already."

He knocked the idea of a one-year spending freeze, which has gained considerable popularity on Capitol Hill, saying that Reagan's proposals would accomplish more long-term deficit reductions than would a freeze. Senate Republicans have been considering a freeze along with selected spending cuts that would cut deficits by substantially more than Reagan's budget would.

Congressional criticism of Reagan's budget proposal appeared to come without regard to geographical, political or philosophical lines, although the intensity appeared to be higher among Democrats, liberals and lawmakers from the Northeast and industrial Midwest.

Rep. Stewart B. McKinney (R-Conn.), a liberal who is cochairman of the Northeast-Midwest coalition budget task force, said, "Come on, nobody can buy this budget . . . this budget is your enemy." It was, he said, "very, very dangerous to the urban areas of the country."

Rep. Bob Edgar (Pa.), McKinney's Democratic counterpart, debunked the notion that it would freeze spending as a whole, saying, "This budget doesn't freeze anything. It is a $40 billion reduction in domestic programs and a $30 billion increase in defense spending."

Rep. Buddy Roemer (D-La.), a conservative southerner, said he was concerned that deficits remain high and added that "defense looks kind of high to me."

Rep. Vin Weber (R-Minn.), a leader of the Conservative Opportunity Society bloc of generally young House Republicans, said he considered the budget a good "starting point" but was concerned about defense-spending levels. He approached deficit reductions from a different angle, questioning whether the "size of deficit reductions should be the ultimate objective of economic policy."

House Budget Committee Chairman William H. Gray III (D-Pa.) said Reagan is continuing to pursue in next year's budget the policies that have produced deficits nudging $200 billion a year.

"The president has given us, essentially, a repeat -- only more so -- of the policies which have created his huge deficits during the past four years," Gray said.

"The president has not met even the goals he set for himself many times prior to now," he added.

While most Senate Republicans remained quiet after weeks of dominating the budget debate, Senate Democrats suddenly found their voices.

"The administration's budget is a wall without windows," said Sen. Lawton Chiles (D-Fla.), ranking Democrat on the Senate Budget Committee. "It tells us what we're up against, but affords no vision . . . . This budget's principal vision of the future is a chain of $170 billion deficits running for the next five years."

Chiles criticized proposed cut in basic scientific research, export promotion, rural assistance, credit protection, law enforcement and energy conservation while, he said, the military remains "awash in too many dollars and too much waste."

Using what he described as more realistic economic projections than those used by the administration, Chiles said Reagan had underestimated deficits by a total of $175 billion over the next five years.

Those Senate Republicans who did speak out generally praised Reagan's overall effort to cut deficits, then criticized specifics of his proposals.

Sen. John W. Warner (R-Va.), a staunch defense supporter, said Reagan's spending cut proposals were "courageous" but added he was disappointed that the defense request was not lower. "Federal spending has to be cut and defense will have to take some of the cuts, otherwise we're headed for serious fiscal problems for the federal government," said Warner, who suggested a real growth increase of 3 percent for the Pentagon, half what Reagan proposed.

Reagan's continued effort to reduce education spending came in for some of the most heated criticism, both from within Congress and from lobbies.

Attacking proposed cuts in education and job-training programs, Rep. Augustus F. Hawkins (D-Calif.), chairman of the House Education and Labor Committee, said spending on advanced defense systems will be wasted if "military personnel are unable to read well enough to learn how to operate them."

Representatives of four higher-education associations predicted hard times for the nation's colleges and universities if Reagan's proposed budget cuts affecting them, including a 25 percent cut in student aid, are approved.

Robert Atwell, head of the American Council on Education, said the proposals would "jeopardize economic growth and the national security by dismantling the historic federal commitment to educational opportunities."

Criticism of proposed cuts in housing assistance also came quickly. William J. Ratzlaff, president of the National Association of Housing and Redevelopment Officials, said they "would represent a devastating blow to the nation's ability to meet its housing and community-development needs."

The National League of Cities said immediate termination of the $4 billion revenue-sharing program for local governments would create "an unreasonable hardship and disruption for all cities."