Conservative House Republicans, stung this spring by President Bush's abandonment of his "no-new-taxes" campaign pledge, said yesterday they could not support a deficit-reduction package that does not include a cut in the capital gains tax rate or that raises personal income tax rates.

"Clearly, the majority of House Republicans would vote against such a package," said Rep. Richard K. Armey (R-Tex.).

It is largely the question of taxes that has stalled the budget talks between congressional leaders and the Bush administration. The bargainers met for three hours last night and early this morning seeking a way to get the talks moving again. They are to meet again today.

Democrats contend that a capital gains tax cut would disproportionately benefit the rich and insist that it be coupled with an increase in the tax rate on the wealthiest Americans.

In hopes of prodding the talks, Senate Minority Leader Robert J. Dole (R-Kan.) recently suggested moving a capital gains cut into a separate legislative package from spending cuts and tax increases. He has also appeared to open the door to raising the top income tax rate, now 28 percent, but does not want to go as high as the 33 percent that Democrats have proposed.

Either move would threaten an agreement's prospects for House approval. Democratic congressional leaders have said any budget accord must win a majority of both parties in both the House and Senate.

"We're not only trying to put together something that makes public policy sense, but could be passed," budget director Richard G. Darman said. "It's a very delicate process of coalition-building."

Conservative House Republicans, who felt abandoned by Bush when he said new taxes were necessary to reduce the deficit, now cling to the president's vow that the budget agreement must encourage economic growth.

"We can't find anything in the talks that has anything to do with growth except capital gains," said Rep. Bill Frenzel (Minn.), the House Budget Committee's ranking Republican. "That will be the key to a number of votes in the House."

House Republicans are also intent on holding the line on tax rates. "Any change in income tax rates becomes difficult to sell among House Republicans," said Rep. Steve Gunderson (R-Wis.). "I don't think Dole's comments were helpful to bringing the budget summit to a conclusion."

Dole's comments are an indication of the frustration he feels over the prolonged talks. A skilled legislator who likes to get things done, Dole last year persuaded Bush to give up his fight for the capital gains tax cut when it threatened to derail a deficit-cutting bill and delay the end of the congressional session.

Further, Dole's relations with White House Chief of Staff John H. Sununu have been strained since 1988 when then-Gov. Sununu helped engineer Bush's victory over Dole in the New Hampshire presidential primary. He did it largely with Bush's "no-new-taxes" campaign pledge and TV commercials depicting Dole as an advocate of tax increases.

Frustration spilled onto the House floor yesterday as conservative Republicans, led by Reps. Robert S. Walker (Pa.) and F. James Sensenbrenner Jr. (Wis.), threw parliamentary roadblocks against what was intended to be a day of action on 37 uncontroversial bills.

Walker said he was protesting "business as usual" in the absence of a budget just one week before the beginning of the new fiscal year.

The House Appropriations Committee is to consider an omnibus spending bill today to fund the government after the Oct. 1 start of fiscal 1991. The measure includes a provision that would delay the Gramm-Rudman-Hollings trigger for automatic, across-the-board spending cuts until Oct. 20.

House Speaker Thomas S. Foley (D-Wash.) said the delay would be needed to hammer any agreement into legislative language and then to enact it. But Foley would not say whether he would try to put off the "sequester" -- massive automatic budget cuts -- in the absence of a pact. "If there is no agreement, we will have a different condition," Foley said. "We don't have any policy at the moment that isn't directed toward an agreement."

Bush has vowed to veto any delay of the deadline. "If you get into the business of suspending and suspending and suspending. . . we'll be at it for 114 years," Darman said.