The Hill reports that — compared with the 112th Congress —fewer incoming members of the House and Senate have signed Grover Norquist’s pledge against tax increases. “About a dozen newly elected House Republicans refused to sign the anti-tax pledge during their campaigns,” notes The Hill, “and another handful of returning Republicans have disavowed their allegiance to the written commitment.”

The implications of this are unclear, but it does bode well for Democrats as they begin to plan for negotiations over the “fiscal cliff” (or slope, given the gradual change in policy if we go “over it”).

Remember, the most important thing about the fiscal cliff is that President Obama holds all of the leverage. If Congress does nothing, the government automatically imposes policies that Republicans fear — higher tax rates and sharp cuts to military spending. In turn, this gives Obama the opportunity to propose his own set of middle-class tax cuts, and dare Republicans to block it — or stand as obstructionists.

The alternative is for Republicans to cut a deal with the president that would involve an end to the Bush tax cuts for incomes over $250,000. Given Obama’s strong position, the GOP can either cooperate or suffer a big blow to its domestic policy priorities.

So far, President Obama has not backed away from his negotiating position. He’s willing to compromise with Republicans on a solution, but — as his spokesman, Jay Carney, noted last Friday — he will not sign a bill that cuts taxes on upper-income earners. That said, neither Carney nor Obama has ruled out a deal that extends the upper-income rates but makes up for it with fewer deductions for wealthy people.

Republicans, perhaps aware of their weak negotiating position, are open to cutting a deal. Speaker John Boehner said that he wouldn’t support higher rates, but that he isn’t opposed to raising more revenue. Paul Ryan echoed him in a recent interview, and Senator Lindsay Graham praised the Simpson-Bowles plan, which assumes higher tax rates than what we currently have.

This is where Norquist comes in. The fewer Republicans committed to the anti-tax pledge, the more likely it is that congressional leaders will be able to bring some Republicans to strike a deal with the administration. What’s more, it seems to be a sign that at least some GOP lawmakers are worried about the political implications of joining with Norquist. You could argue that the refusal to consider a tax increase — represented best by the “10 to 1” moment during the Republican presidential debates — contributed to the public’s sense that the GOP was most concerned with the wealthy.

After four years of fighting an anti-tax crusade — and losing with the reelection of Barack Obama — the GOP, or at least elements of it, seem ready to chart a slightly less radical path.

Jamelle Bouie is a staff writer at The American Prospect, where he writes a blog.