The House yesterday approved stopgap funding to keep the government operating through the rest of this fiscal year, which will end Sept. 30. The vote was 299 to 103.

But the so-called continuing resolution faced possible trouble in the Senate, where several Republicans were reported last night to be considering amendments on busing and other issues that could delay final action until present interim funding expires March 31.

The House action came as Reagan administration officials and congressional Democrats continued fencing inconclusively over who should take the first step toward resolving their continuing impasse over the budget for next fiscal year.

Testifying before the House Budget Committee, Treasury Secretary Donald T. Regan said the administration is going to have to raise its deficit projection for fiscal 1983 and invited congressional efforts to cut the deficit, suggesting "some flexibility" within the administration on tax increases. He reiterated, however, that the administration would await a move by Congress before moving itself.

Regan said he would "probably" support efforts to modify the controversial new law allowing leasing of corporate tax breaks but offered no encouragement to Democrats who are pushing for President Reagan to take the lead in compromising on several other major points, including postponement or reduction of the 1983 individual tax cut.

He pointed out several times that congressional committees are rejecting Reagan's proposed spending cuts while railing at the projected deficits. In an angry exchange, Rep. James Albon Mattox (D-Tex.) countered that the administration had "welched" on promises to balance the budget. "It's members of your party who suggested we welch on our tax cuts," responded Regan, "and we are not going to do it."

Regan said he wanted a "real, no-smoke deficit" of about $90 billion for next year but refused to be pinned down on what the deficit is likely to be in a revised assessment that the administration is to submit to Congress by April 10. He said it would exceed the $91.5 billion that Reagan projected in January, and other administration sources have said that it is likely to exceed $100 billion. Committee Democrats contended the figure is more like $130 billion even if Reagan were to get all the deficit reductions he has proposed, which is unlikely.

"Even the smoke is surrounded by smoke," complained Rep. Les Aspin (D-Wis.).

In the fashion of other administration officials, Regan said he was "looking forward to a genuine bipartisan effort" toward reaching a budget accommodation but stopped short of committing the administration to any specifics.

When Rep. Norman Y. Mineta (D-Calif.) confronted him after the hearing with an assertion that "we're just going to be at loggerheads" until someone can persuade Reagan to compromise, Regan said, "I feel there are ways . . . . We're trying to search out what are the ways." Mineta said after the exchange that he wasn't encouraged.

Meanwhile, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), throwing water on the current Republican strategy of probing for an accommodation first in the Democratic House, said the first move must come in the Republican Senate. He reiterated that he has no intention of moving toward a budget compromise "until I see action from the Republicans."

The resolution that the House passed yesterday is the least of Congress' money problems, although Reagan's veto of an earlier stopgap funding bill closed the government for a day late last year in a dispute over spending cuts. This time leaders had hoped to extend the earlier measure without change, leaving the fight over spending cuts and other deficit reductions until later in the spring, probably in connection with a debt-extension bill that may be needed by mid-May.

The resolution provides funding for six major departments and the Postal Service, along with an assortment of executive branch agencies, for which regular appropriations bills have not been approved. The departments are State, Justice, Commerce, Labor, Treasury and Health and Human Services.

During brief debate on the measure, Rep. James M. Collins (R-Tex.) threatened to try to get the bill sent back to committee for addition of an anti-busing rider. A vote for the resolution would be a "vote for busing," Collins claimed. But he was outmaneuvered, and the measure passed without a direct vote on the busing issue.