Labor, urban and civil rights leaders are in imminent danger of losing a battle to salvage a federal budget they once called inadequate.

The danger grew this week as the leaders tried in vain to garner White House and liberal Senate support to restore at least $1 billion of $10 billion in urban and social programming funds cut from the Carter administration's original budget by the Senate Budget Committee. The revised budget resolution goes to the Senate floor Monday.

"Things look awfully grim," said Thomas Cochran,, deputy executive director of the Conference of Mayors.

"We don't have any amendments in place, we can't seem to get anyone at the White House to defend the administrationhs own budget . . .Things don't look good at all."

Similar complaints came from others of the labor-urban-civil-rights coalition.

"I thought we had our act together, but it looks like we don't," said a ranking official of the National Urban League.

"The fear is justified," said Howard Paster, chief lobbyist for the United Auto union. "The Carter budget is woefully inadequate. But now, in the Senate (budget) committee, that woefully inadequate budget has been cut to the bone."

Coalition leaders said they had been depending on Sens. Daniel P. Moynihan (D-N.Y.), Donald W. Riegle Jr. (D-Md.) and Howard M. Metzenbaum (D-Ohio) to offer floor armendments restoring some of the cuts to housing, nutrition, and public employment programs. But the senators' response was that such an effort would be futile in an austerity-minded Congress.

Even if a restorative amendment is introduced on the floor, coalition and congressional sources say there is every likelihood that it would be opposed successfully by Sen Edmund Muskie (D-Maine), chairman of the Budget Committee.

"In the past, Sen. Muskie's habit has been to preserve the recommendations of the Budget Committee," said James Conroy, committee spokesman.Sen. Henry Bellmon (R-Okla.), the committee's ranking minority member, usually joins Muskie in opposing amendments to the committee's recommendations, Conroy said.

"No one can say what they will or won't do in the future. But there's been nothing to indicate that they will change their practice," Conroy said of Bellmon and Muskie.

In their dealings with the White House, coalition leaders admitted, they find themselves in something of a quandary. In the beginning, they had harshly criticized the administration for giving them too little. Now, they said, they have been place in a position of begging the White House to help them get that "too little" back.

The administration's apparent aloofness stems from its memory of the coalition earlier stinging criticisms, as well as from the political fact that the Senate Budget Committee has the administration boxed in, coalition leaders said.

The committee used a different set of economic assumptions to come up with a budget that seems to be in line with the administration's proposed $29 billion federal deficit for the next fiscal year. Yet the net effect of the committee's different economic projections was to strip nearly $10 billion from social and urban programs included in the administrationhs budget, according to coalition leaders.

"Now, the administration believes it would have to increase the proposed deficit to add anything to the Senate bill," said Cochran."But they feel they can't do that because of the public concern with inflation."