Even before President Barack Obama won reelection last week, Republican leaders said they would not support a tax increase on the wealthiest Americans as a way to resolve the looming “fiscal cliff.”

But at least one popular conservative voice has said that policy is a mistake, not only for the economy, but for the future of the Republican Party.

During an appearance on Fox News Sunday, Weekly Standard Editor Bill Kristol said the congressional Republican leadership needs to stop “falling on its sword to defend a bunch of millionaires” and give in to Obama’s demand for increased tax rates on incomes over $250,000 as party of any debt deal.

“I think honest debate, fresh thinking, leadership in the Republican Party and the leadership in the conservative movement has to pull back, let people float new ideas. Let’s have a serious debate.  Don’t scream, and yell over what one person says,” Kristol said. “You know what? It won’t kill the country if Republicans raise taxes a little bit on millionaires. It really won’t, I don’t think."

House Speaker John Boehner has called any tax hikes of any kind “unacceptable,” even though he still insists Congress can find some other way to raise revenue, a sentiment that has been repeated by Senate Minority Leader Mitch McConnell.

So far, the only plan offered by Boehner is similar to the tax proposal presented recently by Republican presidential candidate Mitt Romney, which was a source of constant speculation and attack during the campaign. The plan aims to boost economic growth, while simultaneously lowering taxes, by making up that revenue through closing certain tax loopholes.

“For the purposes of forging a bipartisan agreement that begins to solve the problem, we’re willing to accept new revenue under the right conditions,” Boehner said during a Nov 7. press conference. “Or does it come as a byproduct of growing our economy, energized by a simpler, cleaner, fairer tax code, with fewer loopholes and lower rates for all?

Like Romney, Boehner has not specified just what tax loopholes could be closed to create the needed revenue.

Although conservatives typically argue that increasing tax rates for the nation’s top earners would impair economic growth by placing a heavier burden on the people they refer to as “job creators,” a recent study by the nonpartisan Congressional Research Service found no correlation between economic growth and tax cuts for the highest earners. In fact, the study concluded those tax cuts spur income inequality.

The New York Times reports the research service withdrew the report from its website after Senate Republicans raised “concerns about its methodology and other flaws.”