Sen. Jon Kyl (R-Ariz.) warned that conservative Republicans shouldn't expect to get exactly what they want on a compromise in a deficit-reduction and debt-ceiling-increase package.

"My Tea Party friends I’m sure appreciate this, but we have to keep reminding ourselves, we don’t control the government. Conservatives are not in charge," Kyl said Friday on Fox News. "And therefore we are not going to get exactly what we want; we have to craft something that leads us in the right direction."

Kyl said the question for Republicans is what kind of bill they can entice Democrats to agree to.

"We can’t dictate the result. Republicans only control the House of Representatives, and twice now they’ve passed something to the Senate and the Senate has said no," Kyl said. "The question is what can be crafted that Senate Democrats will say yes to, because they are half of the legislative equation here."

Kyl's comments come as House Republicans and Senate Democrats race to raise the debt ceiling ahead of the Aug. 2 deadline when the Treasury Department projects the U.S. would otherwise default on its loans. Thus far, though, both chambers have been at odds about what should be in a debt-ceiling increase bill.

In the same interview, Kyl said he's less optimistic about Congress extending the debt ceiling because of "absolute intransigence" by Senate Democrats.

"My gut tells me that we are in a different position than we were even a week ago, where I was very optimistic that we would avoid the Aug. 2 problem," Kyl said. "I am less certain of that now, because there seems to be absolute intransigence on the Senate Democrat side."