In a flurry of last-minute arm twisting, President Reagan and his White House lieutenants cut deals right and left to win House approval of their budget alternative, in some cases reversing their crusade to cut spending.

The high-level horse-trading for Democratic votes included concessions by Reagan on sugar price-support legislation, federal aid for Conrail, medical aid for the poor, student loans and the Clinch River fast breeder reactor in Tennessee, among other items.

The administration was putting a different spin to it yesterday -- Office of Management and Budget Director David A. Stockman said there were no deals, only "accommodations" -- but the outcome was the same. Reagan's stunning victory was clinched by White House largess.

"I went with the best deal," said Rep. John B. Breaux (D-La.), one of 29 Democrats who joined the Republican side Thursday on a key procedural vote on the Reagan package. Somebody wondered if that meant Breaux' vote could be "sold." No, Breaux responded, "It can be rented."

In California, where Reagan is vacationing, White House press spokesman Larry Speakes said, "Compromise is part of the political process. . . . I'm sure not going to stand here and say we didn't do a little compromising, but I can tell you it's not significant in dollar value." By White House count, Reagan made 19 calls to legislators before the vote.

Breaux' "deal," as he understood it, was an administration commitment to accept potentially costly price supports on sugar -- part of pending farm legislation that the White House heretofore has not supported. Louisiana is a major sugar-cane producing state.

Another of the four Louisiana Democrats who sided with Reagan, Rep. Wilbert J. (Billy) Tauzin, said that he, too, was swayed by Republican promises that the administration would accept whatever sugar-support plan emerges from Congress later this summer.

Stockman said the sugar issue was one of the items "brought to our attention" Thursday. "We listened and took them into consideration."

To prevent defections, the White House agreed to at least four budget-boosting changes sought by a dozen moderate Republicans, according to Rep. Bill Green of New York. These included about $350 million more for Medicaid, $400 million more in energy assistance for the poor, $260 million in mass-transit operating subsidies, and additional federal support for Conrail, Green reported.

The administration also agreed to loosen its proposed eligibility restrictions on the guaranteed student loan program, opening the way for more upper middle-income families to qualify. The agreement eased an earlier White House-backed proposal to impose a strict needs test for subsidized loans that would have affected 1.3 million college students.

Stockman told reporters yesterday that "there were adjustments made all the way through this . . . hundreds of adjustments. A few occurred yesterday [Thursday]."

He said the situation on the House floor just before the voting Thursday on the budget package was "highly unique" and "volatile."

"Nobody really knew where those last 10 votes were," Stockman said. On the key vote, substituting a Republican plan for the Democrats', 29 Democrats helped Reagan to a 217-to-210 edge.

The situation apparently was so volatile that top-level Department of Agriculture adies were uncertain yesterday just what promises, if any, the president had made on the sugar-support program sought by legislators from cane and sugar beet-producing states.

"We know there has been some talk between the president and House members and that the president said he would work on a sugar program, but we don't know if there is a commitment," a USDA official said. "Secretary [John R.] Block has told us today that he is willing to work with Congress and listen to what they have to say."

Stockman added, "It depends on what kind of sugar program, if any, emerges in the farm bill." Pending House and Senate bills include support for sugar that would cost consumers as much as $2 billion in higher prices next year, according to USDA analyses.

The White House had made concessions earlier, as the Republican budget alternative was in preparation. The controversial Clinch River fast breeder reactor project, which is strenuously opposed by Stockman as a waste of federal funds, nonetheless receives $230 million more in the Republican budget plan. The increase in offset in part by cuts elsewhere in the nuclear energy budget.

Many of the Democrats who bolted did so as fiscal conservatives who simply prefer the Reagan economic approach to their party's. Rep. Ralph M. Hall, one of nine Texas Democrats who sided with the president, said, "My district is overwhelmingly for Reagan. My mail is 90-10 for his budget proposals. . . . My thrust has been to support the president and give him a chance."

Another Texas Democrat, Rep. Charles Wilson, conceded he was going to stick with his party on the key procedural vote Thursday, but a telephone call from the president helped persuade him otherwise. Wilson said the president told him, "You've gone this far with me, it would be a shame after we took all this heat to lose it now."

But Wilson said Reagan also asked him, "Is there anything you're really interested in that you'd like to talk about?"

Yes, replied Wilson, synfuels. The administration's sharp cuts in federal subsidies for these projects troubled him.

The congressman said the gist of Reagan's reaction was "My door's open. Come on over and talk when this is over."