House Democrats, weary of being scolded by President Reagan for ignoring his budget, agreed yesterday to bring it to the House floor--but as the vehicle for passing something else.

The strategy, as explained by Budget Committee Chairman James R. Jones (D-Okla.), is to use the budget that Reagan proposed last February as the legislative vehicle for consideration of two substitutes, one each from the Democratic and Republican leaderships.

Only if neither of these two alternatives is approved would the House vote on Reagan's original budget, which is now projected by congressional budget experts to entail a deficit of $122.2 billion, substantially higher than the three major budget alternatives rejected by the House last week.

Reagan's budget was unanimously turned down by the Republican-controlled Senate Budget Committee last month and has found few if any champions, Republican or Democratic, in the House. But Reagan and Treasury Secretary Donald T. Regan criticized House Democratic leaders over the weekend for ignoring it in their scramble, thus far unsuccessful, to find a passable alternative.

"Well, we may just do it," an obviously exasperated House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) told reporters yesterday morning as he responded to Reagan's charges of budget sabotage with a similar charge of his own, accusing the president of primary responsibility for last week's budget failures.

Republican Whip Trent Lott (R-Miss.) said O'Neill was playing "cute"--"fun politics," he called it--but Republicans on the Budget Committee did not object to Jones' proposal, pending a conference of all House Republicans today.

Rep. Delbert L. Latta (R-Ohio), ranking Republican on the committee, said he had no objection to the strategy but asked the committee to hold off action until after the conference. Jones, who had been prepared to report out Reagan's budget yesterday, agreed.

Almost lost in the shuffle was Jones' proposal of last week that the House move instead toward a bipartisan split-the-difference compromise. Jones said the White House rejected the notion on Tuesday, adding that it is now "improbable if not impossible" to achieve a bipartisan compromise.

Just back from their Memorial Day recess, House leaders of both parties were only beginning to put together drafts of new budget proposals, and the outlines were sketchy. O'Neill talked of a "true" Democratic budget, shorn of compromising gestures, and Latta said a Republican budget would probably be "to the right" of the the GOP budget that was rejected along with all the rest in a marathon session that lasted until the early hours of last Friday.

Lott said the Republicans would aim for a lower deficit without increasing taxes beyond what they proposed last week, presumably meaning more domestic spending cuts. Last week the Republicans proposed $20 billion in tax increases, the lowest of the three major alternatives.

Both sides agreed that Medicare would probably be shielded from heavy cuts in the second round on the budget. It was a surprise vote of the House to block any Medicare cuts that triggered the turmoil that brought all the budget alternatives tumbling down last week.

The House wasn't even officially back in session from its Memorial Day recess before recriminations over last week's fiasco started gushing forth.

First, O'Neill delivered an angry, bitter response to Reagan's charge over the weekend that House Democrats were responsible for defeat of all the proposed budget alternatives, and then Republicans lashed back in kind.

"If the administration was as good at passing budgets as it is at passing the buck, we would not have the problem we have now. . . . In the end it was the president himself who scuttled the budget last week," said O'Neill.

Majority Leader James C. Wright (D-Tex.) was even more acerbic, accusing the president of pursuing a "rule or ruin" budget strategy. "He Reagan doesn't think anything is a compromise unless he has dictated it. . . . He has sort of a regal notion about the presidency," said Wright.

More specifically, O'Neill accused the president of having told Reps. Denny Smith (R-Ore.) and Bill Archer (R-Tex.) that he wanted no budget at all if the House voted down the Republican alternative, which was sponsored by Latta and Minority Leader Robert H. Michel (R-Ill.).

"The message came from California--with him in his swivel chair and high boots enjoying the sunshine while we were here till all hours of the night toiling away--the message came, only the Latta bill," said O'Neill.

Smith denied O'Neill's allegation, however, saying Reagan had called him last Wednesday but never suggested a no-budget strategy.

"He Reagan didn't have to pass the word," said Latta, explaining that House Republicans never had any intention of supporting any of the alternatives to the GOP-drafted budget proposal.

Minority Whip Lott also rejected suggestions by O'Neill and Wright that Republicans were ready to support one of the other budget alternatives before Reagan got into the act.

"That's baloney. There are some things worse than no budget," said Lott. O'Neill, he added, is "just trying to mask disarray in his own party."

Lott did confirm, however, that the White House rejected a proposal made by Jones on Friday, after all the budgets were shot down, to split the difference between the defeated Republican and Democratic proposals.

"I have the clear impression it was rejected by the White House," reported Lott, who said he agreed with the White House position on grounds that the Republican proposal itself was a compromise that could be stretched no further.