The Senate yesterday refused to choke off debate on a bill to enforce the 1968 fair housing law, but supporters have not given up hope of passing it before Congress quits for the year.

A motion to limit debate won, 51 to 39, but that was nine short of the 60 needed to invoke cloture. Supporters have scheduled a second cloture vote today and a third tomorrow, if necessary. Some held out hope they can draft a compromise bill that will pass.

Senate Majority Leader Robert C. Byrd (D-W.Va.) told the Senate before the vote that if cloture were invoked he would keep the Senate in session until the bill was passed. Congressional leaders have set tomorrow as a target to adjorn Congress for the year but "we are under contract to the American people" until Jan. 3, Byrd said.

But everything would have to work better than it has for the fair housing bill to pass before the 96th Congress expires. The measure is considered the most important civil rights legislation since the voting rights act of 1965. It would give meaning to the 1968 law that forbade housing discrimination but provided no real enforcement powers.

The major dispute has been over procedures for enforcing prohibitions against discrimination in the sale or rental of housing. Civil rights groups want discrimination halted by administrative orders as the quickest and simplest procedure. This was approved by the House and by the Senate Judiciary Committee. But opponents contend a more orderly procedure would be through the federal courts.

Efforts to move the bill out of the Senate committee dragged on for months. And then floor action was delayed before the November election for fear the issue would hurt reelection chances of senators.

Finally, at the start of what is expected to be the final week of the session, supporters tried to call up the House-passed bill, hoping to pass it unchanged and thus avoid a conference with the House to settle differences.

The cloture issue before the Senate is on a preliminary motion to take up the bill. If approved, each senator would be limited to one hour's debate, then, unless a compromise is worked out, there could be another filibuster against the bill itself which would require another cloture vote.