These concerns would be less acute for Mr. Romney if a candidate like Mrs. Bachmann won Iowa. She has less of a national profile and her victory might be viewed as more of a one-off. Mr. Perry, for instance, could well survive a second or third place finish there, hoping to regroup in South Carolina or Florida. That means that Mrs. Bachmann and Mr. Perry would continue to split the conservative vote for some period of time, allowing Mr. Romney to clear his New Hampshire hurdle at a minimum.

Unfortunately for Mr. Romney, Mr. Perry’s national surge does show some signs of transferring into Iowa. The only poll there since he officially entered the race shows him ahead of Mrs. Bachmann, with 21 percent of the vote to her 15 percent, with Mr. Romney stuck in between at 18 percent.

The question for Mr. Romney is whether his New Hampshire lead is robust enough to survive a win by Mr. Perry in Iowa. If not, Mr. Romney will need to involve himself more in Iowa — whether he’s playing to win the state or simply to meddle in it, hoping somehow to harm Mr. Perry at the expense of Mrs. Bachmann and other candidates that would be less of a threat to him.