Anyone who thought Republicans were too focused on spending cuts in the "fiscal cliff" negotiations should brace themselves for what's next.

Tuesday's votes on the "fiscal cliff" deal divided the GOP: More than half of House Republicans voted against it, primarily complaining about its lack of spending cuts. Yet on the Senate side, all but three Republicans supported the measure.

A couple of the Senate's most conservative Republicans say they understand why their House counterparts opposed the bill -- it's littered with special-interest giveaways, was secretly drafted in the dead of night and extends spending on programs like unemployment insurance without paying for them. At the same time, those senators say, those House Republicans may have been too concerned about their outsider, tea party reputations to accept the overwhelming upside of the bill -- making the Bush-era tax rates permanent for nearly all Americans.

"This is not meant to reduce the deficit," Sen. Jim Inhofe, R-Okla., told CBSNews.com about the "fiscal cliff" deal. "This was meant to reduce taxes. The deficit is a different issue."

The nation's spending habit, however, is exactly the issue that will be on the table in a matter of weeks from now, when Congress will have to raise the debt limit, as well as reconsider the "sequester" spending cuts that were only put on hold for two months in the "fiscal cliff" bill.

Sen. Ron Johnson, R-Wis., another conservative who voted for the "fiscal cliff" deal, said voters can expect to see "a strongly united Republican party coming out of this."

"I think what the American public is going to see is President Obama's campaign pledge," he said. "He made the rich pay their fair share -- he got that. Now it's very legitimate for Republicans to demand and see what is the other part of his 'balanced approach'... His tax increase, at most, will close 5 percent of the deficit. What's the other 95 percent? What's his plan to save Social Security? To save Medicare?"

A few weeks ago, many hoped the "fiscal cliff" negotiations would result in a balanced, comprehensive approach to the nation's fiscal issues. Everything seemed to be on the table: entitlement reform, the debt limit, strategic spending cuts with which to replace the sequester, and new tax revenue.

The ultimate deal, brokered by Vice President Joe Biden and Senate Minority Leader Mitch McConnell, R-Ky., was much more limited. Still, some conservatives saw plenty to be pleased with.

Inhofe said he was "in shock" Congress managed to pass an extension of the farm bill, a permanent fix to the alternative minimum tax, the "doc fix" for Medicare reimbursement rates and an extension of the child tax credit, among other things. He also hailed the limited increases in the estate tax and the capital gains tax, which could have gone much higher. "The only bad thing in this thing from a conservative standpoint: they've expanded unemployment insurance too far," he said.