Republican lawmakers say they will only vote for a bill to avert a government shutdown if the bill also defunds Obamacare. Andrew Harrer/Bloomberg via Getty Images

President Barack Obama said he would veto a House budget bill that seeks to defund Obamacare in order to avert a government shutdown.

The announcement came Thursday, a day ahead of a possible vote on the bill.

Obama, speaking Wednesday to business executives at a meeting of the Business Roundtable, said, "You have never seen in the history of the United States the debt ceiling or the threat of not raising the debt ceiling being used to extort a president or a governing party and trying to force issues that have nothing to do with the budget and have nothing to do with the debt."

Some House Republicans have threatened to force a government shutdown unless the next stopgap bill to fund the federal government also defunds Obama's signature health care law.

While raising the possibility of a government closure on Oct. 1, certain GOP leaders and key forces in the tea party drive against Obamacare acknowledged that the latest plan won't fly in the Democratic-controlled Senate.

Senate Democrats have the votes to strip off the health care provision and kick the stopgap measure right back to the House. Still, Republicans who are ardently oppposed to Obamacare are persisting in their message that the the president's Affordable Care Act should be dismantled.

"Harry Reid (D-Nev.) will no doubt try to strip the defund language from the continuing resolution, and right now he likely has the votes to do so," said Sen. Ted Cruz, R-Texas. "At that point, House Republicans must stand firm, hold their ground and continue to listen to the American people."

Republicans in the House spent Wednesday talking about how hard they would fight to derail Obamacare on the eve of its implementation.

A more likely outcome, though, would be that the House would vote to pass a funding bill stripped of the health care provision and send it to Obama to avert a shutdown. Top GOP leaders in the House and Senate made it clear they have no appetite for a shutdown showdown.

"I don't think that any reasonable person thinks there's anything to be gained by a government shutdown," Sen. John Cornyn, R-Texas, said. "Rather than a shutdown of government, what we need is a Republican victory in 2014 so we can be in control. I'm not sure those are mutually compatible."