While it appears that the bipartisan compromise budget will now squeak through the Senate, that doesn't mean fiscal battles are over in Washington, says Ben White, chief economic correspondent for Politico and a CNBC contributor.

None other than House Budget Committee Chairman Paul Ryan, R-Wisc., who forged the budget compromise for the GOP side, is making noise about the debt ceiling, which will have to be raised again next year, White writes on CNBC.com.

Ryan let it be known over the weekend that the GOP will attempt to wring policy concessions out of the Democrats in return for approval of a debt limit increase.

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"We as a caucus . . . are going to meet and discuss what it is we're going to want out of the debt limit," Ryan told the "Fox News Sunday" program. "We don't want 'nothing' out of this debt limit. We're going to decide what it is we're going to accomplish."

So what will the GOP go for? "There will likely be pressure from the right to again use the debt limit to take some kind of bite out of Obamacare," White asserts.

"Whatever they try to add will almost certainly be rejected by the White House and congressional Democrats, setting the stage for a possibly ugly debt limit fight," he adds.

Less than a week ago, optimism about bipartisan cooperation blossomed after Ryan and his Senate counterpart, Patty Murray, D-Wash., reached a budget agreement.

"It is certainly a good start to what would be welcomed relief from the fiscal dysfunction that has defined Washington," Craig Dismuke, chief economic strategist at Vining Sparks in Memphis, Tenn., tells Reuters.

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