Boehner said a demand to tie extension to job-creation measures has still "not been met."
"The Republicans are not just asking for pay-fors," Pelosi said during a press briefing.
Coats and Portman implored Democrats to find an offset for cost of jobless benefits.
In a 60-37 vote, the Senate ended debate on a motion to consider the bill.
Democrats say jobless benefits will remain at the forefront, regardless of Monday's vote.
“We have to be a country committed to leaving nobody behind in this recovery," Sperling said.
Reid says the two issues will be considered separately when Senate returns.
The president emphasized that those out of work "aren't looking for a handout."
President Obama on Tuesday accused Republican critics who oppose extending federal unemployment...
The Senate on Tuesday moved forward with a bill to extend federal unemployment benefits for three...
For Democrats, it's a way to shift away from problems with ObamaCare.
Paul also said that any extension would also need to be paired with job-creating policies.
The Senate majority leader has called the benefits a top priority.