The budget crisis that has paralyzed the government has produced a political crisis that has paralyzed Republican members of the House.

Split by their own president's disavowal of his -- and their -- credo of no new taxes and torn further by a near civil war among their leaders, the 176 members of the House Republican Conference appear to be undergoing a collective identity crisis. On one side are those Republicans who see themselves as part of a governing coalition with the GOP White House; on the other are those who see themselves as an insurgent opposition within the Democratic-controlled Congress.

"It's a fundamental conflict," observed Thomas E. Mann, director of governmental studies for the Brookings Institution. "The governors and the opposition types are drawn up aginst each other along battle lines."

"I do not know where we go from here," lamented Rep. Jack Buechner (R-Mo.), who compared relations within the House Republican Conference to those of a warring family that stays together only because it cannot afford the economic strain of breaking up.

The war broke into the open last week when a majority of House Republicans, led by their second-ranking leader, Minority Whip Newt Gingrich (R-Ga.), defied President Bush and helped defeat a compromise budget plan proposed by the administration and a bipartisan group of congressional leaders. Though the House GOP briefly reunited to sustain Bush's veto of a stopgap spending measure to keep the government operating, the strains quickly reappeared on Sunday.

Divisions over whether and how to negotiate with Democrats on a new budget resolution paralyzed the House GOP late into the night. Minority Leader Robert H. Michel (R-Ill.) was eager to proceed to conference with the Democrats to keep the process moving, but he had only scattered support among junior GOP leaders. Those lawmakers opposing him figured Democratic conferees would simply ram through their proposal with little heed for GOP demands for deeper domestic spending cuts and assurances of a capital gains tax cut.

In the end, Democrats convened and concluded the budget conference without the presence of the House GOP representative, Rep. Bill Frenzel (R-Minn.). Early yesterday morning, the House approved the new budget plan, 250 to 164, with 32 Republicans supporting it and 136 voting against it.

Moderate Republicans aligned with Michel believe that, by opting out of the process over the weekend, they have given the Democratic-controlled Ways and Means Committee what Rep. Marge Roukema (R-N.J.) called "a blank check" to write Democratic legislation implementing whatever budget agreement is finally reached.

Gingrich's wing of the party, said Roukema, has "badly harmed the president and certainly dispirited our leadership."

But other Republicans say their party's long-term interests could well be served if the revenue and spending legislation is covered with Democratic fingerprints just before the November congressional elections.

"If they want to go to the country with a budget that is largely taxes, that's fine with me," said Rep. Mickey Edwards (R-Okla.). "I'll even pitch in to buy them air time."

The stakes in this GOP schism go well beyond the immediate issue of the fiscal 1991 federal budget. They also involve control of the House Republican leadership once Michel retires, probably in 1992, and whether Republicans will soon gain majority status in an institution they haven't led since the first Eisenhower administration.

"The accommodationist wing is not on the ascendancy," said Rep. Chuck Douglas (R-N.H.), a Gingrich ally. "The proof of that is we are willing to take on our own White House."

But more moderate GOP members rue what one called the Gingrich wing's "rule or ruin" strategy as so divisive that it cuts Republicans out of governing altogether.

"We can't just fall back on 'Hell no, no new taxes,' " said Rep. Fred Grandy (R-Iowa). "That's a popular campaign theme in our conference but it has nothing to do with governing."

But Gingrich is clearly playing to a larger national audience beyond Capitol Hill, as illustrated by his and his allies' newly populist rhetoric stressing fairness and equity. The Georgia Republican is even exploring a deal that would lower the capital gains tax rate while raising the marginal income tax rate for the wealthy -- a compromise that would fly in the face of many fund-raising letters he has sent this year pledging everlasting opposition to higher taxes.

Which faction of the House GOP will benefit from this year's budget debate depends greatly on the shape of the coming tax and spending-cut legislation and on whether Bush endorses it.

Should Bush work with Democrats and Senate Republicans for enactment of a package of tax increases and spending cuts to implement the House-passed budget agreement, it would undercut Gingrich and his wing of the party. But if Democrats produce legislation unacceptable to the White House, Gingrich's strategy of confrontation may be validated.

All of this is feeding speculation about Gingrich's future and whether he may be challenged for the whip's position when Republicans elect their leaders again in December.

"It's a great mistake to write off Newt," said Mann. "I don't underestimate the extraordinary frustration in the House Republican Party."

But working against Gingrich, at least for now, is the ire of Bush administration officials at what they see as his treachery. As Tom C. Korologos, a lobbyist who frequently works Capitol Hill on the administration's behalf, said, "You don't go around {angering} the barracudas in this town very long and survive."

Staff writer Don Phillips contributed to this report.