Senate Republicans blocked an attempt to put new Democrat-backed unemployment benefits up for a vote on Tuesday, but Senate Majority Leader Harry Reid said he'll attach the benefit extension to the upcoming war supplemental spending bill.

Last week the House passed the 13-week extension of unemployment benefits, and replaced a requirement of 20 weeks of work to qualify for unemployment with a two-week work requirement.

Republicans say the extension is costly, they object to the proposed work-requirement change, and they say the benefit extension is unnecessary when some states like South Dakota and Wyoming have unemployment rates below 3 percent.

"It's unfortunate that the Senate was stopped from even considering a bill to give a little more help to hurting folks all across this country," said Senate Finance Committee Chairman Max Baucus, D-Mont. "Unemployment numbers are at unacceptable levels, and this unemployment insurance bill is a commonsense response to the real problems that working families are facing in these tough economic times."

The war spending measure could be sent to the Senate from the House as early as this week. President Bush has threatened a veto if it comes to his desk in the House floor's form.

The Senate had passed a different version of the benefit extension, but it did not contain the House's shorter work period requirement.

The House legislation would extend the average $300-a-week benefit check by 13 weeks for all unemployed people who exhaust their regular 26 weeks of benefits. Jobseekers in high unemployment states — Alaska, California, Michigan and Rhode Island, for example — could get an extra 13 weeks on top of that.

The Congressional Budget Office estimated that if the House bill became law, about 3.2 million Americans would collect $11.7 billion in extended unemployment benefits over the life of the extension.

Congress has extended unemployment benefits during periods that turned out to be recessions: twice in the 1970s, again in the early 1980s and 1990s, and most recently from March 2002 through December 2003.

FOX News' Trish Turner and The Associated Press contributed to this report.