President Reagan's austerity budget got a double shot of fresh momentum yesterday as Speaker Thomas P. O'Neill Jr. (D-Mass.) virtually conceded it will pass the Democratic House, and Senate Republicans edged closer to a resolution of their dispute over projected budget deficits.

O'Neill's pessimistic assessment of the chances for a ydemocratic budget alternative caught many members by surprise. Apparently seeking to head off any adverse impact, House Budget Committee Chairman James R. Jones (D-Okla.) issued a statement later saying O'Neill had an "erroneous perception of how some members are leaning."

Jones predicted the vote would be "very close," and some Republicans agreed that the outcome of the House vote on the budget, which is expected late this week or early next, is not yet certain.

O'Neill remarks on the budget alternative drafted by Jones' Budget Committee came as Congress returned from its two-week Easter recess and Reagan prepared to address a joint session of House and Senate tonight on his economic program.

Reagan's campaign for his budget during the recess had a "tremendous impact" and "many of the Democrats" will vote with the president when the budget comes to the House floor later this week, O'Neill told reporters.

"I can read Congress. . . . They go with the will of the people, and the will of the people is to go along with the president," said the speaker. "I've been in politics a long time," he asserted at another point," and I know when you fight and when you don't." Added O'Neill dispiritedly: "Time cures all ills."

O'Neill, who has enjoyed cordial relations with Reagan since the start of his administration, was also severely critical of the president. Expressing doubt that Reagan would consciously cut a program for vaccinating children against disease and hand it over to the states, as his budget proposes to do, O'Neill said, "The president of the United States doesn't know what's in his own bill."

The House will have two main choices when the budget comes to the floor, probably Thursday. One is a White House-blessed "bipartisan" version of the Reagan budget, which calls for more extensive savings than Reagan did but adds a few sweeteners like more money for veterans and comes up with less of a deficit. The other, drafted by Budget Committee Democrats and supported by the Democratic leadership, provides more money for social programs than Reagan did and less of a tax cut than Reagan did and less of a tax cut than he wants, with about half the deficit that the president envisions.

The budget sets spending and taxing pargets for fiscal 1982 -- essentially guidelines, with some enforcement provisions, for authorizations and appropriations that will come later in the year.

In the Senate, Republicans claimed to be on the verge of resolving an embarrassing dispute that sidetracked Reagan's budget just before the congressional recess began. Three of them joined Democrats on the Senate Budget Committee in defeating the preliminary budget for 1982 because, the GOP trio complained, it would not put the government on the path to a balanced budget in 1984, as Reagan has promised.

After meeting with Sen. William L. Armstrong (R-Colo.), leader of the group, Budget Committee Chairman Pete V. Comenici (R-N.M.) said he expected final details would be worked out in time for the committee to approve the budget today. As of late yesterday, only Sen. Charles E. Grassley (R-Iowa) had not agreed to go along.

The budget will project a balance by 1984, Domenici indicated, but only by assuming billions of dollars in unspecified cuts and other general savings. The administration was not forced to pledge specific future budget cuts, and Domenici noted that any provisions for future years were "advisory" in any case.

The plan anticipates savings of about $7 billion from reducing waste, fraud and abuse throughout the budget, $5 billion from expanding the president's authority to rescind appropriations, $7.5 billion from accepting the administration's defense spending figures (the committee said earlier that they were to low) and $1.9 billion from anticipating that the Pentagon will not spend all the money that it says it needs for pay raises.

In addition, there will be about $22 billion in totally unspecified spending cuts that the administration will be expected to make in fiscal 1983 and 1984. Together these unspecified and semi-specified cuts will add up to roughly the same $44.7 billion deficit that had been projected earlier in the rejected budget draft.