Washington (CNN) -- While Senate Majority Leader Harry Reid, D-Nevada, indicated that a vote on the Senate jobs bill could come at any time, it is now expected to take place Wednesday.
Earlier Tuesday, Reid said he was "confident" that the Senate could "work out a reasonable time to vote on this. ... Otherwise, we'll have to do it really late tonight or very early in the morning."
Jennifer Duffy, senior editor of the Cook Political Report, said that both parties and both chambers have "incentive to get something done" soon.
Peter Beinart, a scholar at the nonpartisan New America Foundation, added that it's nearly impossible for Republicans to vote against a bill helping Americans save or pick up jobs.
"It's kind of extraordinary that you have this permanent filibuster against everything -- even stuff like jobs, which should be less controversial than health care," he said.
On Monday, the Senate passed a key procedural vote to push the $15 billion jobs bill to a vote. Five Republicans -- including newly minted Sen. Scott Brown of Massachusetts -- aligned with Democrats to pass the bill 62-30. Sen. Ben Nelson, a Democrat from Nebraska, was the sole Democrat to vote against it.
The Senate bill is a scaled-down version of an $85 billion draft bill that was later scrapped for Reid's $15 billion plan.
The bill exempts employers from Social Security payroll taxes on new hires who were unemployed; funds highway and transit programs through 2010; extends a tax break for businesses that spend money on investments, such as equipment purchases, among other items.
The bill, however, does not extend the deadline to apply for unemployment benefits and the COBRA health insurance subsidy. The House, in passing its $154 billion bill last year, included $79 billion in funding to extend unemployment benefits and a COBRA extension.
On Tuesday, Reid said he would be "asking consent" by the Senate for a separate bill calling for a 30-day extension for "expiring tax provisions, including unemployment insurance, COBRA, flood insurance and a number of other important issues."
If something isn't done, around 1.2 million Americans will run out of benefits after February 28.
"The first critical battle will be between Senate and House Democrats, especially on many of the issues like COBRA," Duffy said. "If Democrats can come to agreement, then Republicans will look at the result and make a judgment about whether they can support it."
House Majority Leader Steny Hoyer said Tuesday that he spoke with Reid about the extensions on unemployment insurance and COBRA. He indicated that the House could pass the Senate jobs bill without going to conference. But he also said it's "accurate to say there will be disagreements."
Reid also said Tuesday that he's working on the next jobs bill, which would be "a small business package ... a very very robust program" that will be bipartisan, just like the current bill. Reid said he hopes to have it done before Easter.
One key differences also to be hashed out between the two chambers includes helps for struggling states.
The House bill provides $23 billion to states in order to save or create an estimated 250,000 education jobs over the next two years. It would also fund positions for $5,000 police officers -- and would provide money to hire and retain firefighters.
CNNMoney Senior Writer Tami Luhby, along with CNN Congressional Producers Ted Barrett, Evan Glass and Deirdre Walsh, contributed to this report.