She estimated that an extension could get done in two or three days if "people would quit worrying about winning elections and worry more about trying to get along and get something done."
Senate Majority Leader Harry Reid (D-Nev.) said on Wednesday that his chamber would remain in session until a deal is reached.
If the House wants to adjourn for the year without an agreement, Speaker John Boehner (R-Ohio) risks "embarrassment" and "humiliation" for leaving town, Reid said.
"Republicans can come to the negotiating table, we welcome them, and work with us to forge a compromise that gives the middle class the relief they need," Reid told reporters.
"Or Republicans can continue to squander valuable time by trying to appease the Tea Party."
While standing next to Collins in a news conference on Tuesday, Senate Minority Leader Mitch McConnell (R-Ky.), was put on the spot about his support for the bipartisan plan — and he didn't exactly give it a ringing endorsement: "I am not in favor of raising taxes on working people. I do favor extending the payroll tax holiday for another year, in conjunction with job creating proposals."
Although the comment was construed to mean he couldn't support the Collins-McCaskill measure, the senator from Maine turned it into a positive on Wednesday.
"Well, actually, what the minority leader said is very consistent with our bill," she said.
"It does not raise taxes on middle-income families, and it does have to create jobs."
As various proposals float around the halls of the Capitol, McCaskill and Collins insist they have a compromise in hand that could pass.
"Well, I think what we all need to start focusing on is trying to find a compromise that can pass," McCaskill said. "That's what Susan and I have done. There are things in this bill I'm not crazy about. Some things she's not crazy about. But it's a real middle ground."
McCaskill called some of the proposals the House is considering "political red meat" and "it's stuff that will divide us further."
"And they know it's not going to pass the Senate," she said. "Why don't we try to focus on a bill that has things that could get support as opposed to trying to divide us for political purposes?"
With divisions evident between Democrats and Republicans and within the GOP ranks, Collins called out President Obama for rhetoric she said "is not helping to bring people together."
"And after all, he's not just a bystander. He is the president of the United States. I'd like to see him show more leadership," she said.
"But what we're trying to do is to transcend all of the partisan rhetoric regardless of which side it comes from, whether it's the Senate, the House or the president. We're trying to get things done for the American people. And we have very little time to accomplish this."