With the House scheduled to vote next week on his request for $100 million in aid to the rebels in Nicaragua, President Reagan has yet to win the support of many key Democrats and Republicans whose votes produced his turnaround victory on the issue last year.

Even Reagan's strongest supporters in the Democratic-controlled House acknowledge that he faces an uphill fight on what many have termed the most important foreign policy issue of this election-year session.

"It's very tough," said Rep. Trent Lott (R-Miss.), the House minority whip, anticipating the scheduled March 19 vote.

To win approval of the proposal, which includes $30 million in nonlethal "humanitarian" aid and $70 million in covert military assistance to the anti-Sandinista rebels, Reagan must make substantial inroads among about 65 House members, divided almost evenly between Republicans and Democrats.

These legislators helped vote down his request last year for military assistance to the counterrevolutionaries, or contras, but later voted for $27 million in nonlethal aid.

House committee votes and interviews last week indicate that Reagan has persuaded several Republicans in the swing group to go along with his latest request -- although it calls for covert military assistance and nearly four times as much money.

The president faces strong resistance, however, among Democrats in the group, many from the South and the Southwest, a region considered in tune with the staunch anticommunist rhetoric that has been the hallmark of Reagan's campaign for this year's package.

Several other factors complicate the president's task:

*The House Democratic leadership scheduled the floor vote to occur before the two-week Easter recess, giving the president little time to mobilize public opinion.

*The proposal will come to the House floor as a single package, not subject to amendment or other legislative tinkering that is often crucial in building a winning coalition among lawmakers who are looking for ways to defend a controversial vote.

*Church and peace groups who adamantly oppose aid to the contras have been the dominant activists on the issue so far, with the public seemingly detached and unconcerned, Democrats and Republicans say.

*The debate centers on foreign policy, but the House measure is in essence a money bill, calling for the expenditure of $100 million in a foreign country -- not an easy proposal to sell in the current budget and political climate.

The net result, many of the Democrats said, is a president pitching an all-or-nothing proposal with far less credibility than he enjoyed last year to a more skeptical audience -- both on Capitol Hill and in the nation.

"The mania is not there that anything you want for defense, let's do it," said Rep. W.G. (Bill) Hefner (D-N.C.). "That's where the climate has changed -- not only in the South, but all across the nation."

As a result, many Democrats and Republicans said that the March 19 vote is likely to be the beginning rather than the end of this year's battle over aid to the contras.

Ultimately, some said, there is likely to be a compromise, most likely framed in the Senate, that would grant some nonlethal assistance tied to strong incentives for increased diplomatic efforts.

"The administration will be dragged, perhaps kicking and screaming, into another position," predicted Rep. Dave McCurdy (D-Okla.), a key moderate involved in compromise efforts.

Much of the current opposition among Democrats stems from assurances they said Reagan made when the House, after earlier rejecting military aid, approved the $27 million nonlethal aid package last June 12 by a vote of 248 to 184.

Chief among those assurances were pledges of diplomatic efforts, both directly with the Sandinista government in Managua and through the four-nation Contadora group, to find a peaceful solution.

Rep. William B. Richardson (D-N.M.), who now characterizes his vote for the aid package last year as "a mistake," said the administration said then that it was "committed to the Contadora process. But the secretary of state told the Contadora ministers to take a walk."

Some Democrats complain that Reagan, rather than making a good faith effort to find peaceful solutions, seems bent on a military campaign. They say he bills the campaign as essential to curbing communism before it reaches America's doorstep but that it has little guarantee of success -- no matter how much money is appropriated -- and no endorsement from the leaders of other Central American nations, including the democracies.

"I wouldn't have a bit of trouble with whatever amount of military aid it's going to take to win," said Rep. Charles W. Stenholm (D-Tex.), who voted for military and nonlethal assistance last year but says he is a reluctant supporter of the current aid plan. "I want to be reassured that somebody else agrees with our game plan," he said.

"If it is this important," McCurdy said of the contra cause, "what are we doing messing around with an untrained, disorganized peasant army when we have our own forces?"

A General Accounting Office report suggesting that much of last year's aid may never have reached the contras is further fueling skepticism about additional assistance.

Some Democrats said they could support a request for more nonlethal aid, but so far Reagan has steadfastly refused to compromise on the current proposal, which McCurdy likened in part to "a $70 million blank check" for military operations.

On the Republican side, Reagan enjoys strong support among southern and most western conservatives. But most of the GOP swing voters are moderates from the Midwest and Northeast, and here the results so far are mixed. Even some who say they will vote for military aid appear to be less than enthusiastic.

One is Rep. Lynn M. Martin (R-Ill.), a member of the GOP House leadership. She said she has become convinced by a series of White House briefings that the administration now has a "serious" plan to combat communism in Central America, which was not her feeling a year ago.

Martin, reflecting the strong isolationist sentiment of her northwest Illinois district, remains a skeptic who is looking for results. But she will vote with Reagan on March 19 -- "once," she said, holding up a single finger.

Rep. Steven Gunderson (R-Wis.) is still not convinced, but is open to persuasion. "You gotta show me," he said, demanding more evidence that the Sandinista government lacks popular support and is exporting violence throughout Central America.

Gunderson is also among those lawmakers who are troubled by the thought of voting $100 million to rebel military forces in a foreign country while his constituents face cutbacks in domestic programs.

"One problem is the president has made the issue $100 million," he said. "Every one of my constituents understands that if you get the same amount in 1987 as you did in 1986, you're doing well. This is not the year to ask for an increase."

Others among last year's swing voters are clearly lost to Reagan.

Rep. Thomas J. Tauke (R-Iowa), a leader of the so-called "92 Group" of House Republican moderates, said he is more convinced than ever that the Sandinistas are "establishing a totalitarian government" in Nicaragua and are "intent on spreading Marxism" in Central America.

But Tauke added that he is now equally convinced that military aid to the contras is not the answer to these developments.

"I don't believe that military assistance will be helpful in resolving that problem and I suspect it could drive the people of Central America toward the Sandinistas," he said.

Lott, whose job as GOP whip is to count the votes, said that to win, Reagan must pick up 12 to 20 of the 40 House Republicans who defected in last year's vote on military aid and enjoy the support of at least 50 Democrats, 10 more than last year.

If the administration is defeated on March 19, he said, "My recommendation will be that we walk away from it and say that House Speaker Tip O'Neill and the Democrats lost Nicaragua."

That, however, is unlikely, no matter what the outcome of next week's scheduled floor vote.

"This is the beginning, not the end," said Rep. Daniel A. Mica (D-Fla.).