Several campaigns question whether Buttigieg really has staying power in those early state polls and are waiting to see if he’ll fall back to earth on his own, without a push. “This is just Pete’s moment,” said Jeff Weaver, a Sanders senior adviser, “and we’ll see, we’ll see whether he stays up or goes down.”

Others suggested Buttigieg’s time facing a barrage of criticism was still coming, and soon. “Just like all the other frontrunners he’ll get his turn,” said Rep. Cedric Richmond (D-La.), co-chair of Biden’s campaign. “He’ll get his body cavity check and people will find the flaws in his [policy] plan, and I think that they’ll see that some of the things are just absolutely unrealistic.”

Meanwhile, Booker campaign manager Addisu Demissie noted that the senator is depending on Buttigieg backers to “vote for us, ultimately” — backed up by polling that finds many Democratic primary voters are still very open to changing their minds about their primary or caucus vote. And in Iowa, the caucus system benefits candidates who can become the second choice of many voters, which can make candidates wary of going on the attack.

Still, Buttigieg’s opponents opened up lines of attack that can be deployed again if his recent rise in Iowa and New Hampshire sticks.