To win over a few Republicans, Democrats will "have to try to figure out a way to get that debt number down."
Senate Minority Whip Jon Kyl (R-Ariz.) said his colleagues are all over the map in the amount of deficit spending they'd accept.
"Republicans aren't monolithic in our point of view," he said. "Some have a higher threshold for deficit spending than others do. I suspect what you'll end up seeing is that some will say, 'Look, we just cannot afford to continue to spend money, especially if we're just bailing states out.'"
States were "warned" not to count on Federal Medical Assistance Percentages (FMAP) funding, "but they did anyway," Kyl said.
He suspects many of his colleagues don't want to borrow more money to give to states "who knew they probably weren't going to get it."
If other Republicans like the most recent modifications, which are still under construction, there might be some who want to support the bill, especially because of unemployment benefits.
"My guess is there is increasing pressure — all of us feel pressure — for those who don't have jobs," Kyl said.
UI might be easier to swallow now for some Republicans as Americans still struggle to find jobs, although Thune said the issue hasn't been whipped and isn't sure about support.
Still, corralling all Democrats to support the bill has been fraught with trouble.
Democratic Sen. Ben Nelson (D-Neb.) has repeatedly said he won't accept any deficit spending and will only back a paid-for measure. Sen. Joseph Lieberman (I-Conn.) also has voiced reservations about the measure and said he isn't prepared to back the bill just yet.
That leaves the Democrats three votes short of the 60 needed to move forward, meaning they'd need to spring at least three Republicans to pass the bill.
Senate Finance Chairman Max Baucus (D-Mont.) told reporters Tuesday that work is being done on the bill, and he can "see the light at the end of the tunnel."
That tunnel has been a long one for Senate Democrats who are crafting their third version of the tax extenders legislation since returning from the Memorial Day recess in early June.