Senate Minority Leader Mitch McConnell (R-Ky.), accompanied by Sen. Lamar Alexander (R-Tenn.) and Sen. John Barrasso (R-Wyo.). (AP Photo/Jacquelyn Martin)

Think the congressional debate over extending the payroll tax is simply a matter of how to pay the cost of doing so?

Think again.

Thursday night’s competing Senate votes on extending the one-year payroll tax holiday – a key political priority for the Obama administration heading into a heated election year – revealed that deep differences exist between the parties not just on how to pay for extending the tax break, but also on whether to continue the cut at all.

The result has been a split among Republicans – and an unfolding debate in which, at least for the time being, Democrats and the White House appear to have seized the upper hand on the issue of taxes.

Until Thursday, the main debate over the payroll tax holiday was expected to be over how to pay for the cut. Leaders of both parties have come out in recent weeks backing the extension, and this week it was anticipated that each party would support its own competing “pay-for” proposal.

That was how a debate last month over repeal of the 3-percent withholding rule on federal contractors played out: Both parties supported the repeal, but Senate Democrats objected to the pay-for proposed by House Republicans. The final compromise included the Republican pay-for as well as a provision that would make the measure more palatable to Democrats -- an amendment to provide tax credits to businesses that hire unemployed or disabled veterans.

But in the latest debate, despite Senate Minority Leader Mitch McConnell’s (R-Ky.) prediction on Tuesday that a “majority” of Republicans in his conference would back some version of the payroll tax cut extension, more Republicans voted against the GOP measure than voted for it.

The 20-to-26 split among Senate Republicans -- one member, Sen. John McCain (R-Ariz.), did not vote – came as a surprise to leadership aides of both parties Thursday night.

And as members’ statements on the vote came in late Thursday and Friday, it became clear that what most Senate Republicans objected to wasn’t their party’s proposed “pay-for,” which included some recommendations of the bipartisan Simpson-Bowles commission such as an additional three-year pay freeze for federal workers and benefit reductions for the wealthy.

Instead, most Republicans who voted “no” on Thursday night said they approved of the “pay-for” proposal but were against extending the payroll tax cut itself – a development that could spell trouble in the Republican-led House, which is expected to take up its own payroll-tax proposal in the coming week.

Republican senators opposing the payroll tax cut extension break down into two main camps.

Some senators oppose the payroll tax cut extension because they believe it would jeopardize the future of Social Security by diminishing the stream of revenue dedicated to the Social Security Trust Fund. At least seven Republican senators Thursday night issued statements citing concerns about Social Security’s solvency as the primary reason for their “no” votes: Republican Sens. Lamar Alexander (Tenn.), Roy Blunt (Mo.), Richard Burr (N.C.), John Boozman (Ark.), Jeff Sessions (Ark.), Mark Kirk (Ill.) and Ron Johnson (Wis.).

“There are 55 million Social Security beneficiaries that will see little or no extra cash from this 2012 tax holiday; instead, the dedicated payroll contributions meant to pay for future benefits are being diverted from the Trust Fund and replaced with Treasury debt that does not even have a AAA credit rating,” Kirk said in his statement.

“Social Security was designed to be independent and free from the danger of Congressional manipulation, and maintaining the firewall between the Social Security Trust Fund and general government funding is the best way to maintain the solvency of this important program. Neither bill protects the Social Security Trust Fund so I voted no,” he added.

While it’s true that the payroll tax holiday would reduce the amount in the trust fund, the law requires that the general fund reimburse Social Security for the amount of the cut, resulting in no net reduction in funding. But some lawmakers of both parties still object to extending the tax cut because it would in effect make Social Security funding subject to the congressional appropriations process.

On top of that, there’s the matter of whether the cut is paid for or not – the former would not result in adding to the debt, while the latter would.

The second group of Republican senators opposing the payroll tax cut extension did so because they said Congress needs to work toward comprehensive reform of the tax code, not short-term fixes. This argument was emphasized Thursday by at least six Republican senators: Sens. Bob Corker (Tenn.), John Cornyn (Texas), Orrin Hatch (Utah), Jim DeMint (S.C.), Mike Lee (Utah) and James Inhofe (Okla.).

“While I strongly support keeping the American taxpayer’s burden as low as possible, especially during the current economic situation in our country, I voted against last night’s extension of the so-called payroll tax holiday,” Inhofe said in a statement. “Our economy and American taxpayers need more permanency to the tax code, not less. This is another example of why comprehensive tax reform that simplifies and lowers the tax burden on American families and job creators is so desperately needed.”

While those senators have advocated for a broader tax reform effort – particularly in the wake of the debt supercommittee’s failure -- it’s worth noting that with the exception of DeMint, all six voted in favor of last month’s measure extending tax credits to businesses for hiring veterans, a bill that was illustrative of the tough task Congress faces in actually reforming the tax code.

In floor remarks after Thursday’s vote, Sen. Jerry Moran (R-Kansas) emphasized both Social Security and the need for a broader tax-reform effort. Sen. Johnny Isakson (R-Ga.) argued that Congress passed the payroll tax cut last year in order to stimulate the economy, and “it didn’t work.” And Sen. Mike Johanns (R-Neb.) said that neither the Democratic nor the Republican proposal “constituted responsible policy making, so I voted against both of them.”

Where does that leave the payroll tax debate, and the larger battle over taxes?

For one thing, it’s worth noting that even though 26 Republicans voted “no” on their own party’s payroll tax plan, the 20 who voted “yes” – combined with the one Republican and the 50 members of the Democratic caucus who backed Senate Majority Leader Harry Reid’s (D-Nev.) proposal – mean that 71 senators have voted in favor of some type of payroll tax cut extension.

That would suggest that any compromise is likely to stand a good chance of passing the Senate, although that could change depending on what the pay-for looks like.

In the House, leaders face the tough task of crafting a payroll tax cut proposal that is palatable to rank-and-file members – which in part explains why on Friday, House Speaker John Boehner (R-Ohio) and other GOP leaders set to work on a broader package that bundles the payroll tax holiday with other measures popular among Republicans, some of which have already passed the House.

As far as the bigger picture goes, the Senate payroll tax vote represents a shift in the debate over taxes. After a summer debt-ceiling debate that underscored the Republican Party’s anti-tax orthodoxy, the fall supercommittee deliberations – in which Republicans for the first time put new revenue on the table -- and now the payroll tax cut debate have made the GOP’s message on taxes somewhat more muddled.

Instead of a battle over tax increases versus no tax increases, the debate has now entered a phase where some Republicans are differentiating between income tax increases versus payroll tax increases and short-term tax changes versus comprehensive tax reform.

While similar debates have played out before in Congress (such as on the ethanol tax credit earlier this year), the latest round marks the first time that the White House has gotten so actively involved on the issue – and with the national spotlight on the issue, the debate on Capitol Hill looks only to ramp up over the coming weeks.

Staff writer Lori Montgomery contributed to this report.