It’s not getting the attention it deserves, but one of the key reasons that the current budget standoff is so politically tricky for GOP leaders is this: They are navigating a very large and persistent opinion gap between GOP base voters and independents, who are sharply at odds with each other over whether they prefer a budget compromise or a government shutdown.

That’s the key finding in two new polls — one from NBC/WSJ, the other from Gallup. They both find, strikingly, that Republicans are the only group that prefers a government shutdown or a breakdown in talks rather than a compromise, even as strong majorities of independents favor a compromise.

The NBC poll asked Republicans and independents: “Do you want Republican leaders in the House and Senate to make compromises on current budget debate, or do you want them to stick to their positions even if it means not gaining consensus on the budget?”

Only 38 percent of Republicans said they want compromise, while 56 percent said they want them to stick to their positions. By contrast, independents strongly favored compromise, 65-30. Strikingly, the numbers represent a shift among Republicans away from desiring compromise: In December, NBC/WSJ polling found that Republicans were evenly divided on whether they wanted their leaders to pursue compromise. Now they tilt strongly against it.

This overall finding is mirrored even more starkly in a new Gallup poll. It found that Republicans are the only group that prefers a government shutdown to a compromise on a budget they disagree with, 51-44. Meanwhile, independents strongly prefer compromise over a shutdown, 60-29.

Bill McInturff, the GOP pollster who helps oversee the NBC/WSJ poll, noted the challenge GOP leaders face in navigating this divide between the GOP base and between independents, who enabled Republican victories in 2010 and will be crucial to the party’s hopes in 2012. “That’s a very precarious gap to negotiate,” McInturff said.

This gap is the key to understanding why John Boehner is bringing us right up to the brink of a shutdown: It’s the best political move available to him under very difficult circumstances. Boehner recognizes that a government shutdown could be politically disastrous to the GOP, since it would risk squandering the party’s recent gains among independents and play into the Dem strategy of winning indys back by painting the GOP as hostage to Tea Party extremists. At the same time, the GOP base is adamantly opposed to compromise.

So Boeher is skirting the edge of a shutdown in order to make it easier to sell an eventual compromise to the base — and to House conservatives — later. By arguing that his willingness to bring us to the brink put pressure on Dems to agree to maximum concessions, Boehner can perhaps limit the fallout a compromise may cause on his right by persuading conservatives that he did everything humanly possible to win all he could and getting them to accept a compromise on the understanding that the bigger battles are yet to come.

Of course, as Jonathan Bernstein pointed out the other day, this is a high-stakes gamble: Brinkmanship has been known to lead, against the wishes of all the players involved, to inadvertent war.