So far, all Republicans and one Democrat, Sen. Ben Nelson (Neb.) have voted against the variations of a the larger bill, leaving it short of the 60 votes needed to move forward.
Proponents have noted the economic impact letting benefits lapse for about 1.2 million people, which is expected to happen at the end of June.
Americans receive an average of $304 a week, providing about $6.7 billion a month in economic stimulus, according to the National Employment Law Project, a group studying the issue.
The Congressional Budget Office has said every dollar in unemployment benefits, is worth a $1.90 to the economy.
In the past, unemployment benefits have not only been routinely extended without being offset but have remained in place until the unemployment rate reaches lower levels, somewhere between 5 and 7 percent. Economists have said the U.S. rate could hover around 8 percent for at least the next year of not longer.
If Congress is unable to extend benefits, all 50 states would lose emergency funding that provides between 34 and 53 additional weeks on top of the state-provided 26 weeks.
Only 11 states could continue with the 13-20 week extended benefits program because triggers based on state's unemployment rate have been worked out separately of the federal program. But at least 20 other states would lose those extra benefits that would provide up to 20 weeks, according to NELP.
Overall statistics on unemployment benefits are off the charts -- 46 percent of 15 million unemployed Americans have been out of work for at least six months, with an average jobless for 34.4 weeks, the highest in history, according to NELP and Labor Department statistics.
A total of 54 percent of everyone who use unemployment insurance exhaust all of their benefits, up to 99 weeks in states with high levels of unemployment.
Senate Minority Leader Mitch McConnellMitch McConnellRepublicans at risk in 2018 steering clear of town halls GOP rep on Trump: 'God has used imperfect people to do great things before' McConnell: 'Winners make policy, losers go home' MORE (R-Ky.) has offered a paid-for version using stimulus money and Sen. Olympia Snowe (R-Maine) suggested a stand-alone version late last week that wouldn't be offset.
No decisions have been made on how to move forward, according to Democratic aides.
Another possibility is the House could put together a bill and send it to the Senate, possibly providing some time for the upper chamber to reach a consensus before leaving town at the end of the week.