Think the congressional debate over extending the payroll tax holiday is simply a matter of how to pay for the benefit? Think again.

Thursday night’s Senate votes on extending the one-year holiday — a priority for the Obama administration — revealed deep differences between the parties not just over how to pay for the payroll tax break, but also on whether to continue it at all.

In particular, there is a split among Republicans — and an unfolding debate in which Democrats appear to have seized the upper hand on the issue of taxes.

GOP leaders set to work Friday on crafting a broad package that would bundle the payroll tax holiday with other measures popular among Republicans, in an effort to appeal to rank-and-file members.

Until Thursday, the main debate was expected to be over how to pay for the payroll tax holiday. Leaders of both parties had backed the extension, and each party was expected to support its own “pay-for” proposal.

But in the end, more Republicans voted against the GOP measure than for it. Most Republicans opponents 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 proposal next week.

Republican senators opposing the payroll tax cut extension break down into two camps. Some believe continuing the cut would jeopardize the future of Social Security by diminishing revenue dedicated to the Social Security Trust Fund.

The second group said they want comprehensive tax reform, not short-term fixes.

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

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 Democrats who backed a proposal by Senate Majority Leader Harry M. Reid (D-Nev.) — yields a total of 71 senators who have voted in favor of some type of extension.

That suggests a compromise could pass the Senate.

Staff writer Lori Montgomery contributed to this report.