Post-shutdown, all eyes on the budget committee

(CBS News) - "There will not be another government shutdown. You can count on that," vowed Senate Minority Leader Mitch McConnell, Sunday on "Face the Nation," adding that the shutdown strategy did not reflect Republican principles.

"Shutting down the government, in my view, is not conservative policy," he told host Bob Schieffer. "I don't think a two-week paid vacation for federal employees is conservative policy."

McConnell's view stands in contrast to that of Texas Senator Ted Cruz, who hasn't ruled out the possibility of another shutdown over ObamaCare. Read more about what McConnell's assessment means for the budget fight ahead in Congress at The Washington Post, United Press International, The New York Times, TIME Magazine, The Wall Street Journal, The Washington Times, Politico, Newsmax and the Financial Times.

The Senate Republican leader also assured host Bob Schieffer that he wasn't worried a primary challenge from the right.

"I've endured millions of dollars of attack ads that have been calling me a right-wing fanatic over the years," he said. "I think my opponents in the primary are going to have a hard time convincing Kentucky primary voters that I'm some kind of liberal." POLITCO and McClatchy picked up the Kentucky Republican's quip.

Sen. Lindsey Graham, R-S.C., appearing later in the broadcast, agreed with Sen. McConnell's criticism of the shutdown strategy.

"As a party, we got to do some soul-searching," Graham said. "The tactic of defunding the government unless he repealed his signature issue was as poorly designed as ObamaCare itself, almost."

The focus, Graham argued, now shifts to finding a long-term budget deal.

"We've got a unique opportunity here after this debacle called the shutdown to reenergize the Congress and maybe get an understanding," Graham said.

Sen. Warner, D-Va., who serves alongside Graham on the budget conference committee created by the bipartisan deal last week, remains optimistic that the committee will find common ground.

"We all know at the end of the day, Republicans are going to have to give on revenues, Democrats are going to have to give on entitlement reform," he said. "We do that, the confidence-building that would take place, I actually believe it would do more for job creation than any other program we've talked about." Read more about our conversation with Sens. Warner and Graham at The Hill and POLITICO.

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    Louise Dufresne is an Associate Producer for Face the Nation.