"He's completely lost control of the Italian bond market in two weeks," said Boockvar. "I think he's going to do his best to verbally calm nerves, but as far as legally using his balance sheet to help, I don't see what he can do."

But some traders appear to see the Italian situation as enough of a red flag to slow the Fed, particularly after the U.K. Brexit vote led to a market correction.

"The market is still pricing in a Fed hike for next month. It's already in the cards. Why would the Fed not raise interest rates, given the kind of economic data we expect this week?" said Chandler. "Where I really see this having an effect is on the back end, the September hike."

Robert Sinche, chief global strategist at Amherst Pierpont, does not see enough damage from Italy to slow the Fed.

"I think this will be a lot of noise, but I've seen this movie three or four times before. Italy stays in [the euro zone], and life goes on. There could be a little more uncertainty over the summer. They've realized that, which is why they pushed up the election to late July/early August," he said.