According to several reports, House Republicans are torn between two choices: Whether to pursue an unpopular Tea Party agenda (which GOP leaders know would go nowhere) or whether to pursue no agenda at all.

Today’s New York Times reports that “no agenda” is emerging as the tentative choice so far. The story depicts the GOP House as a tamed institution, just hoping to get through the year without anyone noticing them. Think I’m exaggerating? Look at this remarkable quote from GOP Rep. Tom Cole:

“The big thing for us is to not be part of the conversation instead of trying to inject ourselves into it.”

Politico also found some support among Republicans for that position, with Senator Richard Burr of North Carolina worrying that if Congressional Republicans pursue a proactive agenda, the GOP presidential nominee will wind up “stepping on us.”

On the other hand, Paul Ryan seems ready to write a budget that will inject House Republicans and their unpopular Medicare plan into the conversation. And it’s unclear whether radical Members have any intention of ceding the limelight to the presidential nominee, especially given that Mitt Romney is almost certain to be that nominee.

In other words, we have basically the same dynamic in the House that we had last year: the Speaker understands that quixotic quests to pass items that Rush Limbaugh’s audience will love but will be highly unpopular with swing voters is probably not the smartest strategy. Especially since those items are doomed to irrelevancy because of the Democratic Senate (not to mention Barack Obama’s veto pen).

So what’s next? Here’s where to look to get clues. We know that about 50 or so Members are dedicated to pushing a radical conservative agenda whenever possible; we also know that Speaker John Boehner and the handful of relatively moderate Republicans either oppose those efforts or realize they’re counterproductive for the party. The question then becomes, what about the rest of the GOP House conference?

Are they more worried about adopting a Tea Party agenda, which could mean swing voters turn on them, imperiling GOP control of the House and endangering their presidential nominee? Or are they more worried about the risks of not doing the Tea Party’s bidding, leading to a RINO label and a primary challenge?

All of this will play out in the negotiations over whether to extend the payroll tax cut and unemployment insurance, and Congress has about three weeks remaining to get those done. The endgame there will provide an excellent hint as to whether we’re in for another year of destructive brinkmanship or if House Republicans are going to lay low and try to avoid being seen.