The deal between the President and the House Democratic leadership worked smoothly yesterday to prevent any dollar changes during floor debate on the $61.3 billion money bill for the departments of Labor and Health, Education and Welfare.

But final passage was delayed as members offered a series to riders to forbid use of the money for - among other things - school busing, abortions and the enforcement of hiring and school admission quotas based on race or sex.

On money, the revived Democratic coalition only had to show its strength once. It smashed, by a 72 to 334 vote, and amendment by Republican Whip Robert Michel (III.) to cut $563.5 million from several major programs in the bill.

Three weeks ago, that same Michel amendment - supported by the President - had lost one vote, 25 to 24, in the House Appropriations Committee.

Speaker Thomas P. (Tip) O'Neill (D-Mass.), before he came to terms on Wednesday with the White House, had worried the Michel amendment might win in a floor vote with Carter's active support.

Upholding their end of the deal, White House aides did not help Michel at all. Thus, the bill remains intact though it contains $1.4 billion more for HEW programs than the President wanted. His part of the deal is a promise not to veto the bill because of that amount.

Another amendment that once had a chance of floor approval would added $40.1 million to the National Cancer Institute. However, it was withdrawn yesterday by its sponsor, Rep. Silvio Conte (R-Mass), as a result of O'Neill's deal with the White House.

Conte said yesterday during debate that he asked the manager of the Labor-HEW bill, Rep. Daniel Flood (D-Pa.), "for assurances that he would compromise on a figure for the cancer institute between the House and the Senate."

Flood agreed, Conte said. Because the Senate figure now stands $88 million above the House amount, Conte said he believed he would get what he wanted "without antagonizing anyone" by putting his amendment to a vote.

A third amendment, by Rep. James M. Jeffords (R-Vt.), to add $240 million to help jurisdictions comply with new federal standards for the handicapped also was withdrawn.

A promise from House Majority Whip John Brademas (Ind.) that hearings would be held to work out the problem was enough to satisfy Jeffords.

After holding off attempts to decrease or increase the funds in the bill, the House voted to strengthen the bill's prohibition against busing. But - amendments pending on other controversial issues, abortion and quotas, caused final action on the bill to be put off until today.

The bill, through and amendment by Sen. Robert Byrd (D.W. Va.) adopted in 1975 and repeated each year since, already prohibits using or threatening to withhold, federal education funds to require busing of any student to a school "other than the school which is nearest the student's home" offering the proper curriculum.

But HEW Secretary Joseph A. Califano Jr., with the backing of a legal opinion by Attorney General Griffin B. Bell, had announced the administration might pursue a policy of withholding funds from school districts that refuse to merge with nearby schools, one predominantly black and one predominantly white, to facilitate desegregation.

Under the process called, "pairing" or clustering" one school might offer, kindergarten through the fourth grade, while the other would offer fifth through eight grades.

The House yesterday moves to block this by adopting, 225 to 157, an amendment by Rep. Ronald M. Mottl (D-Pa.) that provided that no funds in the bill could be used or withheld to require busing because of merging, pairing or clustering of schools.

Mottl accused HEW of doing a "legalistic somersault" to cirumvent the Byrd amendment.

However, Mottl and others admitted the prohibitions in the bill don't really stop busing, since they do not affect court-ordered busing, only HEW attempts to compel busing under the 1964 Civil Rights Act. Mottl admitted only a constitutional amendment could stop court-ordered busing. But his rider let the house go on record against busing in general.

Today's fights will center on an amendment by Rep. Robert Walker (R-Pa.) that would provide that none of the funds in the bill could be used to force any institution or individual to meet hiring or admission quotas based on race or sex.

HEW is bitterly resisting the amendment which officials believe would wipe out virtually all attempts at so-called affirmative action.

The bill also provides that no Medicaid funds can be used to perform abortions unless the life of the mother is in danger.

Pro-abortion forces, though an amendment by Rep. Louis Stokes (D-Ohio), will try to strike that provision of the bill which they believe discriminates against the poor who could not otherwise afford abortions.

But HEW and the Carter administration oppose the Stokes amendment and favor withholding Medicaid funds for abortions. Ultimately, this issue, too, will have to be resolved by the Supreme Court, which is expected to rule on the matter soon.

Finally an amendment may be offered which could help Secretary Califano follow President Carter's example in simple living. Recent news stories reported that Califano had hired, under another job description, a person who primarily cooked for him at HEW.

Under an amendment which may be offered by Rep. Allen Ertel (D-Pa.), none of the money in the bill could be used to pay for either a cook or a chauffeur for Califano or any other HEW official.