The Senate yesterday killed its fair housing bill and picked up speed toward adjournament as conservative Democrats joined most Republicans in choking off the swan song of the liberals in the 96th Congress.

By 54 to 43, six votes short of the 60 needed, the Senate refused to end a week-long filibuster led by Republican conservatives against the controversial civil rights legislation.

The action followed a last-gasp request by Senate Majority Leader Robert C. Byrd (D-W.Va.) for a few, more hours to work out a compromise satisfactory to wavering conservatives. The Republicans spurned the request, wiping out whatever flickering chance there was -- and some participants said it wasn't much -- to reach an accomodation.

Moments later, Byrd followed through on an earlier pledge to shelve the bill if the cloture move failed, thus putting Congress onto a fast track toward adjournment of its lame-duck session this week.

The Senate then quickly ended another filibuster over a federal judgeship and went on to a bill extending the program of revenue sharing with local governments for another three years.

To resolve another civil rights dispute that was also holding up adjournment, lawmakers were working on a compromise under which the Carter administration would hold off school busing suits in exchange for stripping anti-busing language from an omnibus spending resolution, which President Carter had threatened to veto if it contained busing curbs.

Having chosen the housing bill for their last stand before relinquishing control of the Senate to the Republicans next month, Democrats were quick to make political capital out of the bill's demise.

"In a month's time," thundered Sen. Daniel P. Moynihan (D-N.Y.), gesturing dramatically toward the Republicans, "it is going to be the responsibility of the gentlemen who blocked this legislation to come forth and give life to it."

Senate Minority Leader Howard H. Baker Jr. (R-Tenn.) had sought earlier in the debate to deflect the Democrats' attack with a pledge that he, as majority leader next year, would push for their housing legislation early in the 97th Congress. "A good bill, not just a bill in name only," Baker told the Senate just before the cloture vote.

But other Republicans made it clear that the controversial enforcement provisions of this year's bill, designed to put teeth in the landmark 1968 fair housing act, would be sharply modified.

The bill, passed earlier this year by a big margin in the House, would have empowdered the Department of Housing and Urban Development to bring legal action to end discrimination in housing transactions, with fines of up to $10,000 for violators.At the end, one of the major sticking points was whether the government would have toprove intent to discriminate. Republicans indicated they would insist on this test in any future legislation, and civil rights groups said it would be unacceptable.

Senate Judiciary Chairman Edward M. Kennedy (D-Mass.), who led the floor fight for the legislation, attempted to lay the blame for the bill's defeat squarely at the feet of the conservative Republicans who will dominate the Senate next year.

"A small group of conservative Republicans who wanted to roll back the clock" led the Republican Party into a "major retreat . . . from its commitment to civil rights," he told reporters after the vote.

To the contrary, responded Sen. Orrin G. Hatch (R-Utah), who led the filibuster against the bill, the whole fight arose over "one of those last-gasp untra-liberal" moves by the Democrats "to impose the federal government on the lives of the people."

While Republicans supplied most of the votes against the bill, it was southern and border state Democrats who made the difference between approval of an earlier cloture motion by a vote of 62 to 32 last Thursday and defeat of the decisive cloture effort yesterday.

The Democrats who switched were Sens. David L. Boren (Okla.), Sam Nunn (Ga.), J. Bennett Johnston (La.), Russell Long (La.), Howell Heflin (Ala.), Robert Morgan (N.C), Lloyd Bentsen (Tex.) and Walter D. Huddleston (Ky.). By contrast only three Republicans -- Sens. Bob Dole (Kan.), Nancy L. Kassebaum (Kan.) and Robert Packwood (Ore.) -- switched their votes.

There were no switches among Washington area senators. On both votes, Maryland senators Charles Mathias (R) and Paul Sarbanes (D) supported cloture, while Virginia Sens. Harry F. Byrd Jr. (Ind.) and John W. Warner (R) opposed it.

In all, nine of the 41 Republicans supported cloture, as did some southerners, including Sens. Ernest F. Hollings (D-S.C.) and lame duck Sen. Donald W. Stewart (D-Ala.), who was defeated for reelection. The hard core of support for the bill included all the Democratic liberals who were defeated in the elections, many of whom will be succeeded by conservative Republicans.

Byrd and Kennedy negotiated with the wavering Democrats almost to the last minute, making concessions that civil rights groups said came close to making the bill unacceptable to them. But it wasn't enough for the conservatives. One source said that Johnston and Nunn were the critical holdouts.

Kennedy forces said the switch of moderate Republicans like Dole, who had been heavily involved in the negotiations, was pivotal in dissuading the conservative Democrats from supporting cloture for a second time. But several Republicans, including Kassebaum, said the Democratic holdouts were the key. Heflin said he thought an accommodation could have been worked out "if we had more time . . . there just wasn't time to work it out."

On the busng issue, Sen. Jesse Helms (R-N.C.), principal backer of an appropriations rider to ban the Justice Department from pursuing busing in school desegregation cases, said he will continue to push for the ban unless the administration agrees to back off busing suits until its term runs out Jan. 20. But he said he will not filibuster to keep the ban, adding that he expects the incoming Reagan adminstration to support his proposal to strip the federal courts of jurisdiction over busing suits. "The bottom line is that we've won."