Alaska Republican Senate candidate Joe Miller thinks so:

“I think there’s an understanding that the mood of the nation has changed in such a way that there is not going to be toleration of business as usual. If that means shutting down the government, so be it. I mean, we’ll do what it takes,” he says. “I think that we will have enough like-minded people coming into D.C. that we’re actually going to be able to accomplish something.”
But is Sen. Mitch McConnell, the Senate GOP leader, open to the possibility of shutting down the federal government? “There was a comment made at breakfast this morning about shutting down the government, and he reacted in a positive way,” Miller says. “I’m not going to quote him, but I think that he recognizes that that’s on the table.”

If the Republicans want to stymie President Obama's agenda, they don't need to shut down the government. But if they want to enact positive policy changes of their own, they do. Or, they need to make a deal with Obama, though any deal that's acceptable to Obama is assuredly unacceptable to the base.

That leaves the threat of a shutdown to force Obama's hand. Of course, the Clinton-Gingrich example has showed this is an extraordinarily weak tool -- the threat blows up on Congress. You'd think Republicans will want to avoid repeating history, but since forswearing the shutdown means abandoning their policy goals, it will be be hard for them not to try.