WASHINGTON - The U.S. Senate's top Democrat and top Republican each voiced support on Wednesday for extending a soon-to-expire $8,000 tax credit for homebuyers, but left unclear when the chamber would act.

There has been general agreement by a significant number of senators, Democrats and Republicans, to get this done, Senate Majority Leader Harry Reid, a Democrat, said on the Senate floor.

The chamber's top Republican, Senator Mitch McConnell, also said most senators support the measure.

I certainly share his view, McConnell said.

The tax credit, which has helped lift the housing market out of its worst slump since the Great Depression, is set to expire on November 30.

While extending the credit may enjoy widespread support, its fate is caught up in a spat between Reid and McConnell over unrelated issues.

Reid had wanted to attach a bill to extend the homebuyer credit as an amendment to a bill to lengthen insurance benefits for unemployed workers. The Senate voted 87-13 on Tuesday to take up the insurance benefit bill, but did not attach the homebuyer tax credit to the measure as Reid had wanted.

Despite that apparent roadblock, Senate Finance Committee Chairman Max Baucus, who has been involved in negotiations over the tax credit, told Reuters late on Tuesday that he expected the Senate would vote on the bill sometime this week.

There are various paths and whichever works first is the one that is going to be followed, he said, referring to the possibility that the Senate could vote on the bill independently or as part of separate legislation.

A spokeswoman for Reid said the unemployment insurance measure could get pushed to next week as lawmakers try to resolve difference over unrelated issues, which would delay consideration of the homebuyer credit extension.

We will get this extension passed, she said.

A report last week showed sales of previously owned homes hit a two-year high in September as buyers rushed to take advantage of the credit before its expiration date. However, a report on Wednesday showed new home sales, a much smaller segment of the market, tumbled unexpectedly last month.

A separate report from the Mortgage Bankers Association on Wednesday showed demand for mortgages has fallen for the past three weeks as buyers move to the sidelines.

A buyer would have to settle before November 30 to take advantage of the tax credit.

(Additional Reporting by Lisa Lambert; editing by Vicki Allen)