(Jonathan Ernst/Getty Images)

As deadlines for a government funding measure and a payroll tax cut extension loom, House Speaker John Boehner (R-Ohio) on Thursday dismissed reports that Democrats have dropped their push for a surtax on millionaires, arguing that Democratic leaders never had enough votes to pass the measure to begin with.

“They never had the votes for their so-called millionaires’ surtax,” Boehner said at his weekly briefing with reporters. “They didn’t even have the votes in 2009 and 2010, when they controlled everything. So, I appreciate the fact that they gave up on their millionaires’ surtax, but they didn’t give anything up because they never had it.”

At a separate news conference Thursday, House Minority Leader Nancy Pelosi (D-Calif.) emphasized that Democrats still view the issue of “shared sacrifice” as of prime concern and suggested that the surtax on the wealthy may reappear at a later date.

“I don’t think they’ve given up on it,” Pelosi said of the millionaires’ surtax. “It’s still something to be considered. This is not the last bill that ever gets passed.”

The exchange came as Congress faces a deadline of midnight Friday to pass a government funding resolution; lawmakers must also strike a deal on an extension of several must-pass measures including a payroll tax holiday before the end of the month.

Boehner said Thursday that House members won’t adjourn for good until both issues are resolved, although the chamber could take a few days off should the action move over to the Senate.

“Once the House passes an appropriations bill to keep our government funded, there’s no reason for House members to sit around here,” Boehner said. “If the Senate acts, I’m committed to bringing the House back — we can do it within 24 hours — to deal with whatever the Senate does.”

“There is absolutely no interest on our part in trying to be strident about this,” he added. “We believe it’s important to keep the government open, and we believe it’s important to finish the work on the payroll tax cut, unemployment insurance and the doc fix.”

Senate leaders on Thursday morning struck a cooperative tone and said they are hopeful a compromise on both measures can be worked out in the coming days. But House GOP leaders have moved forward with plans to progress a funding bill with Republican support alone, which, if it passed, could mean the House would have some time on its hands as the White House and leaders of both chambers work out a compromise.

Boehner said that he believes there’s an “easy way to resolve our issues” on the payroll tax cut extension — Senate leaders should bring the House-passed measure to the floor and allow members to offer amendments to the bill.

“No more show votes; I think it’s just time to legislate,” he said.

But Pelosi argued Thursday that the House GOP payroll tax plan, which includes a provision that would speed up a decision on the Keystone XL oil sands pipeline, was “doomed from the start” and that if Republican leaders proceed with their plans on the funding bill, they are “exacerbating the crisis” surrounding the government funding fight.

“I hope they have the votes for it,” she said of the GOP funding plan.

As the deadline for Congress to pass a funding bill looms less than 36 hours away, Boehner told reporters that “there’s no need to shut down the government” and cited Senate Majority Leader Harry Reid’s (D-Nev.) floor remarks Thursday morning as a sign that Democrats “may not do that after all.”

Pelosi, too, said that she “certainly hope(s) that there won’t be” a shutdown, but pointed the finger at Republicans, who she argued must “come to their senses” and compromise on a deal.