Although President Reagan won a significant budget victory in the House Thursday, his spending cuts must still survive a minefield of opposition in Congress before they become final.

The House approved about $114 billion in domestic program cuts over the next three years, but it did so in the abstract, and key committee chairmen who must next report out implementing legislation are balking at many of the new totals and in some cases vowing to resist to the end.

Adding to their resolve are the many groups that would suffer from the cuts and are hoping to staunch their losses by fighting back in the legislative committees.

House Majority Leader James C. Wright Jr. (D-Tex.), noting that many Democratic committee chairmen were reluctant to make large cuts sought by Reagan last year and felt their authority was usurped in the process, said there is "a greater sense of rebellion among them I'm sure this year."

Even in the Republican-controlled Senate yesterday, there was fresh evidence of dissatisfaction with some of the cuts contemplated in domestic programs. The Senate Agriculture Committee refused to approve several key changes in the food stamp law without which it would be impossible to meet the budget goals in the House resolution.

The next skirmish comes as the conference on the budget resolution seeks to work out a compromise between the House's $114 billion in cuts over three years and the Senate's $93 billion. But these figures are only overall targets, and the specific reductions must then be worked out by the legislative committees.

And it is in these committees, where many of the members have spent their careers building up the affected programs, that members are lying in wait to reverse the cuts voted Thursday.

Rep. Henry A. Waxman (D-Calif.), chairman of the House subcommittee that handles Medicaid, said yesterday, "These cuts are too large, indefensible, and damaging to the program, and I do not plan to develop and support legislation to make cuts of such magnitude." The House budget resolution proposes to cut $6.6 billon over three years from Medicaid, which provides medical assistance to the poor.

Rep. Andy Jacobs (D-Ind.), chairman of the subcommittee that oversees Medicare, said: "I'm already working to repeal the part I'm responsible for. My posture is to repeal what was done" on Thursday. Under the House proposal, Medicare, government medical insurance for the elderly, would be cut $11.5 billion over three years.

Rep. Harold E. Ford (D-Tenn.), chairman of the House public assistance subcommittee, likewise suggested it might be impossible to achieve the $3.3 billion in savings over three years that the House ordered for welfare. "I'm not certain we can find the cuts," he said.

Rep. Frederick W. Richmond (D-N.Y.), chairman of the House subcommittee with jurisdiction over food stamps, said the $7.7 billion three-year reduction in food stamps and child nutrition envisioned in the House budget resolution would be a "total disaster" and he plans to resist as much as possible during legislative deliberations.

Even Sen. Robert J. Dole (R-Kan.), chairman of the Senate Finance Committee and of the Senate food stamp subcommittee, indicated unhappiness with some of the proposed reductions, especially in food stamps. Dole has worked closely with the Senate Republican leadership in trying to get many of the cuts sought by the president, but he said yesterday, "The food stamp cuts are far too high . . . not realistic at all."

Dole noted that the House level of Medicaid cuts was more than triple the Senate's three-year $2 billion reduction, and he considered the $2 billion "about max." He said he would do his best to meet the compromise targets that will be set by the House-Senate budget conference, but he wants the less severe Senate version to prevail.

If the legislative committees don't make the cuts outlined in the budget resolution, once these are set by the House-Senate conference, the final decision then goes back to the floor of each chamber.

House Budget Committee Chairman James R. Jones (D-Okla.) has hinted to colleagues that he does not expect all the legislative committees to follow through with cuts outlined in the budget resolution. In that case, he would seek to force the Republicans to take the lead--and the heat--for further program cuts on the floor.

"It's going to be almost exclusively up to Republicans to enforce these very deep cuts in social programs," said Jones.

Already, many lobbying groups are gearing up to fight back in the legislative committees, which in the House are dominated by Democrats.

Laurie Fiori, a lobbyist for the giant American Association of Retired Persons, said the group will work to block cuts in Medicare, Medicaid and food stamps. The American Federation of Teachers was gearing up to oppose education cuts. And Nancy Amidei of the Food Research Action Center said of the prospective reduction in food stamps, "we're going to fight it."

Dale Lestina, a lobbyist for the National Education Association, said the nation's largest teachers' group would now attempt to recapture in the appropriations committee the education money that would be slashed by the budget resolution. "This business never ends," he said. "What one gains today you have to defend tomorrow."