President Barack Obama again pressured House Republicans to put a “clean” government spending bill up for a vote Monday, challenging House Speaker John Boehner's claim that the funding bill lacks sufficient support to pass.

"My very strong suspicion is there are enough votes there" to pass the government funding legislation, he said during an unannounced stop at FEMA National Response Coordination Center in Washington, D.C.

"Hold a vote. Call a vote right now. Let's see what happens.''

President Barack Obama calls on Republican House Speaker John Boehner to bring a clean continuing resolution to the floor for a vote. Obama made the remarks Monday in Washington, D.C., while visiting FEMA headquarters.

Boehner said on Sunday that a government funding bill without substantial changes to the president’s health care law would not pass the GOP-dominated House.

The administration – as well as numerous whip counts by media outlets, including NBC News – disputes that claim.

Obama also reiterated Monday that he will not allow the GOP to tack major policy changes onto a measure to raise the debt ceiling before the government runs out of borrowed funds on October 17.

"We can't threaten an economic catastrophe in the midst of budget negotiations," he said.

Senate Democrats are poised to introduce legislation as early as today to raise the debt ceiling with no strings attached, according to aides. That measure would extend the nation's borrowing authority until after next year's midterm elections.

That's a measure Boehner says also can't pass the House. He insisted Sunday that the Republican-led lower chamber would not approve a measure to raise the debt ceiling without first negotiating additional measures to address causes of the nation's debt.

Republican House Speaker John Boehner addresses the chamber Monday, calling on President Barack Obama to negotiate on the debt ceiling.

“I'm not going to raise the debt limit without a serious conversation about dealing with problems that are driving the debt up,” Boehner said on ABC's This Week.

The renewed back-and-forth comes as a pair of new polls show that Americans are unhappy with both sides for the dispute, although congressional Republicans are carrying more of the blame.

A new Washington Post/ABC poll shows that 70 percent of respondents disapprove of how congressional Republicans are handing the budget fight, versus 61 percent disapproving of congressional Democrats and 51 percent disapproving of the president's role in the impasse.

A poll from Pew shows that Americans blame Republicans more than Obama for the shutdown by a margin of 38 percent to 30 percent.

As the GOP continues to argue that Obama is refusing to negotiate over the shutdown, Democrats insist that the "clean" bill already represents a compromise because it funds the government at lower levels than some liberals in Congress wanted.

"The bill that is being presented to end the government shutdown reflects Republican priorities," Obama said during the stop at FEMA. "It is the Republican budget."

Republicans immediately responded to the FEMA visit by urging Obama to green-light a piecemeal measure that would temporarily fund the agency during the shutdown. Senate Democrats have balked at talking up the piecemeal funding bills, and the president has threatened to veto them, saying the entire government should be reopened.

The House passed one such measure late Monday to restore funding for the Food and Drug Administration during the shutdown. The legislation, the ninth piecemeal funding bill approved by the House, passed 235-162.

Obama said Monday that FEMA remains prepared for national disasters but “their job has been made more difficult” by the shutdown. He said that Florida and the nation’s Atlantic coast “dodged a bullet” when a potential storm along the coast disappeared but that many FEMA workers called back from furlough to prepare for the storm will now be sent home again.

The stop was part of the administration’s continuing effort to highlight the impact of the ongoing federal shutdown on government services. He visited a Maryland small business last week to speak about the shutdown’s effects on the economy.

NBC's Kasie Hunt contributed to this report.

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