Almost a quarter of voters who supported President Obama’s 2012 re-election would not have backed him if they'd known his promise that Americans could keep their existing health plans under Obamacare wasn’t true, according to a Republican poll.

The national survey, conducted by Wilson Perkins Allen Opinion Research, the same firm that advises Sen. Ted Cruz, R-Texas. According to the poll, 23 percent of voters who supported Obama would not have voted for him had they known that Obamacare would force insurance companies to cancel non-compliant health policies despite Obama's promise.

"The 2012 election would have been different had Obama voters been aware that their health care plans would be cancelled due to the Affordable Care Act,” the firm wrote in a memo shared with the Washington Examiner Friday.

The broken promise hurts Obama across a broad cross-section of the public, the poll shows. About 23 percent of men, 31 percent of women under 54 and 17 percent of women over 55 also said they would not have voted for Obama if they'd known.

The poll also shows that Republicans now have a 6 percentage point edge with voters over Democrats, a reversal from a month earlier when a government shutdown was dragging down Republican approval ratings. Independent voters, a crucial swing voting bloc, preferred Republicans by a 39 percent to 30 percent margin.

The WPA poll was conducted Monday through Wednesday when congressional Republicans were on the offensive against Obamacare. It has a 3.5 percent margin of error.

The question asked of respondents who voted for Obama in 2012 was:

“As you may know, millions of Americans have lost their insurance plans despite President Obama’s promise that, quote, ‘if you like your plan, you can keep it.’ If you knew in 2012 that this promise was not true, would you still have voted for Barack Obama?”