President Bush is coming under increasing pressure from fellow Republicans to abandon all but the pretext of conducting budget talks and to set the stage next week for a full-scale confrontation with Democrats on the deficit issue, administration and party sources said yesterday.

The first showdown in the budget battle endgame could occur Wednesday or Thursday when the House is expected to consider a measure that would push from Oct. 1 to Oct. 20 the deadline for the Gramm-Rudman-Hollings law's automatic, across-the-board spending cuts. A senior official said Bush "won't let them get away with delaying this until the election is over."

White House and congressional budget negotiators met again yesterday and agreed to another session Sunday after further discussion of a proposal by Senate Minority Leader Robert J. Dole (R-Kan.) to split any deficit-reduction plan into two packages, one with spending cuts and tax increases that would reduce the deficit and the other with tax cuts, including a capital gains tax cut, and new spending programs.

Dole refined his proposal yesterday to include a provision that says if either measure were defeated the other would be defeated as well. That all but ended speculation that Dole would try to abandon Bush's demand for a capital gains tax cut, the issue in the budget talks that Democrats have described as a break for the rich and the main roadblock to agreement.

Bush yesterday described the budget showdown as "nine days and counting." He called on Congress to produce a deal, reiterated his desire for a capital gains cut and avoided taking any position on the Dole proposal.

Bush's statement showed no softening in his demands as he warned he will not accept "a temporary quick-fix that sweeps this problem under the rug."

As the budget talks dragged through the week, administration officials appeared to harden their stands and to begin positioning themselves for the political and economic chaos that might follow a breakdown in the negotiations.

Officials met Wednesday and Thursday with House GOP leaders to discuss how to block any attempt by Democrats to avoid immediate implementation of across-the-board cuts if there is no budget agreement. The discussion, according to participants, centered largely on whether the administration has the votes to sustain a presidential veto of legislation designed to delay the cuts.

House Republicans are surveying their members on the issue and Rep. Robert S. Walker (R-Pa.) said at the White House, "The initial numbers look pretty good." An administration official said, however, that unless Bush "sets the stage now, by going public with the Democratic refusal to deal in good faith, we're going to have a hard, hard time when the disaster stories from {the automatic cuts} hit."

Charles Black, spokesman for the Republican National Committee, said yesterday that "even President Bush's patience is growing thin. This is a critical week. He is prepared to take off the gloves, present a budget of his own for an up or down vote and then lay the blame for this on the Democrats where it belongs."

The RNC sent a statement from Black to dozens of news outlets, threatening that Bush and the GOP "will describe in stark terms how the Democrats' big spending habits threaten the havoc of a radical sequester and economic recession."

Sources said the decision to issue the statement reflected mounting frustration in GOP political circles that Democrats have been successful in attacking the administration's tax proposals as a break for the rich and that the White House has not effectively responded.

One Republican operative called the situation a "sound-bite massacre" for the GOP.

The provision to delay the deadline for automatic cuts is part of an omnibus spending bill for the federal government from the beginning of fiscal 1991 on Oct. 1 through Oct. 20. It also includes additional Pentagon funding for the Persian Gulf operation and other provisions the White House wants.

An indication of the impasse that has developed came yesterday when the negotiators were asked by reporters what they had eaten for lunch. "We couldn't decide," Dole replied.

Staff writer John E. Yang contributed to this report.