A project by Republicans on the Senate Budget Committee to show President Carter how his $532 billion budget could be slashed by $9 billion has collapsed in failure, committee sources said yesterday.

To the delight of the committee's majority Democrats, the Republicans were unable to agree on how to trim the fiscal 1980 budget deficit to $20 billion from the $29 billion estimated by Carter.

"Their last meeting ended in a shambles," a source acquainted with the GOP project said. "I guess it about a balanced budget than actually putting one together."

Sen. Pete Domenici (R-N.M.), a balanced-budget advocate who helped organize the GOP project, was reluctant to discuss what happened but acknowledged the effort had been abandoned.

"It is very hard to get agreement," Domenicl said.

The original hope, Domenici said, was to get the committee Republi spending program that would be offered as a GOP alternative to the budget resolution being put together by the committee.

That resolution, which sets Congress' preliminary spending ceilings for the budget, must be submitted to the Senate by April 15.

"We gave up on the idea of offering a Republican budget," Domenicl said. "We just couldn't agree on whether it was a good idea to have a Republican budget."

Sources said the Budget Committee's Republican staff had put together a draft budget that held the deficit for the fiscal year beginning Oct. 1 to $20 billion.

But when the committee's eight Republicans discussed the draft they could not agree on the specific spending cuts proposed in the draft, sources said.

"Their target was to get the deficit down to $20 billion but when they couldn't get below $25 billion they just gave up," one source said.

Among federal programs listed for deep cuts in the GOP draft were said to be countercyclical revenue sharing, food stamps, transportation, community development and foreign aid.

"One guy would want a lid on Social Security benefits but another would reject it," a source said. "Another would want to cut urban aid but another wouldn't and that is how it went."

The Republicans here were said to have tried the defic-cutting project as a trial run for a Republican balanced budget offering to the Budget Committee next year.

The committee has been mandated by a new law to submit nonbinding balanced budgets for fiscal years 1981 and 1982 and to explain the effects of a balanced budget on revenues, spending, employmenty.

That provision was added by the Senate last month to legislation to raise the national debt ceiling temporarily from $798 billion to $830 billion.

In addition to Domenici, Republican members of the Bellmon (Okla.), Bob Packwood (Ore.), William L. Armstrong (Colo.), Nancy L. Kassebaum (Kan.), Rudy Boschwitz (Minn.), Orrin R. Hatch (Utah) and Larry Pressler (S.D.).