The Senate voted yesterday to break an adjournment-threatening filibuster against fair-housing legislation, and Democratic leaders vowed to stay in session as long as it takes to get final action on the disputed bill.

At the same time, Senate Majority Leader Robert C. Byrd (D-W.Va.) moved to derail and end-of-session effort by the Senate Appropriations Committee to give Congress a pay raise, saying it might be justified but "I will not stand for it at this time."

By late evening, it appeared that the Senate, mired ever deeper in its filibuster problems, would not be able to adjourn today as planned.

Negotiations on the antidiscrimination housing bill broke off during the evening, with participants planning to resume today but with little apparent hope of an immediate breakthrough to permit a final vote on the housing bill.

There were these other developments as both houses groped -- without success in the case of the Senate -- to move legislation swiftly enough to meet today's target for adjournment of the 96th Congress:

Drowning out earlier talk of a possible challenge by Byrd's leadership after the Republicans take over the Senate in January, Senate Democrats unanimously elected Byrd as their minority leader, keeping Sen. Alan Cranston (Calif.) as party whip and Sen. Daniel K. Inouye (Hawaii) as caucus secretary.

The House voted, 189 to 186, to kill legislation that would have forced major auto makers to start putting airbag safety devices in at least some cars by 1983.

The Senate Finance Committee voted to extend the government's borrowing authority through only March 31, rather than Sept. 30 as the Carter administration requested, so the Senate can be assured of a vehicle for passage of a tax-cut bill early next year. With a new debt-ceiling measure required early in the year, a tax cut could simply be attached to it, as the ever resourceful Finance Committee chairman, Russell B. Long (D-La.), explained it. The debt ceiling through March 31 would be $956 billion. The current ceiling, which could be reached by the end of the year, is $925 billion.

House-Senate conferees agreed on a $160.1 billion defense appropriations bill, including $300 million for a new strategic bomber. The record military money bill for fiscal 1981 is $5.6 billion more than President Carter requested, reflecting Congress' mounting concern over the nation's defense capabilities and increasing generosity toward the Pentagon.

The House passed and sent to the Senate, which is expected to pass it, a bill authorizing $22 billion in mass transit aid over the next 10 years.

The Senate's 62-to-32 vote to invoke cloture against the three-day fairhousing filibuster was a qualified victory for civil rights forces, raising their spirits but stopping far short of actually ending the delaying campaign by conservative Republican opponents of the measure.

The bill's advocates gained 11 votes -- mostly southern and border-state Democrats -- since the first cloture vote on Wednesday. This gave them two votes more than the 60 necessary to choke off debate on bringing up the bill.

However, under complicated Senate filibuster rules, opponents led by Sen. Orrin G. Hatch (R-Utah) could continue to delay for days. Even after cloture is invoked, the Senate has up to 100 hours for debate, and a second filibuster could be launched even after that. Moreover, Hatch claims to have up to 300 amendments ready for introduction if necessary to string out the filibuster even longer.

Negotiations, at one point involving Hatch and civil rights leaders who have been hovering outside the Senate chamber for most of the week, continued through much of the day without any apparent resolution.

The bill, described by its advocates as the most far-reaching civil rights legislation in a decade, would put teeth in the landmark 1968 Fair Housing Act by empowering the Department of Housing and Urban Development to initiate housing discrimination cases before administrative law judges.

Previously HUD was limited to a mediation role in housing bias cases, and court suits could be brought by the Justice Department only in a limited number of cases involving broad patterns of segregation.

In a compromise move, the bill's supporters agreed to have the cases tried by federal magistrates, who are judicial appointees, rather than by administrative law judges, who are part of the executive bureaucracy and thus suspect to some.

But opponents, including Hatch, continued to insist to specific provisions in the bill for trial by jury in housing cases and proof of intent to discriminate before a landlord could be found guilty -- demands that were unacceptable to the bill's supporters.

The House has already passed a fair housing bill, and any major modifications could mean difficulty in an conference, although Democrats on both sides of the Capitol appear eager to make the bill the centerpiece of their lame-duck session. Moreover, civil rights leaders fear that the Reagan administration and incoming Republican Senate will be less hospitable to such legislation next year.

In any case, the Senate Democrats appear to be making it their swan song and preparing to blame the GOP lavishly if the measure dies in a filibuster. a

So long as the bill is pending in its present parliamentary posture, the Senate can take up no other legslation. This means that several appropriations bills, revenue-sharing authorization and stopgap funding for the government until Congress can complete action on appropriations next year are, in effect, being held hostage for action on the housing bill.

At a press conference after the Democratic caucus, Byrd said it was the feeling of the lame-duck Democratic majority that Congress should not adjourn without action on the housing bill as well as revenue sharing, defense and agriculture appropriations, the stopgap funding measure and debt limit extension.

Acknowledging it may not be possible to complete action on all the bills by today as originally planned, Byrd said the Senate would meet tomorrow and if necessary, "Monday and beyond."

"Our contracts haven't expired and we still have our work to do," said Byrd, accusing the conservative Republican filibusterers of "obstruction tactics" in fighting the bill.

On the highly controversial pay raise issue, Byrd said he will move to defeat it when it comes to the Senate floor in conjunction with the interim government spending measure. The Appropriations Committee tacked it on to the measure Wednesday night at the suggestion of Senate Minority Whip Ted Stevens (R-Alaska). The pay raise, which the House has already rejected in its version of the measure, would raise salaries of members of Congress from $60,662.50 to $70,900 annually and provide comparable increases for federal officials at GS15 and above.