Protest. There was only one last-ditch demand Republicans in Congress rallied around in the end-of-year budget negotiations that concluded today — a black line in the tar sands drawn by the conservative legislative machine. In order to approve a payroll tax-cut extension — a measure that the GOP’s tax-hating ranks already support in theory and that’s widely understood to be an effective stimulus to our sagging economy — Republicans held out on a single, make-or-break issue.

Democrats could have a two-month extension of the payroll tax cut — but only if they let Republicans pursue a gambit to get the Keystone XL pipeline approved.

In other words, GOP lawmakers told Americans, “Sure, we’ll kick in a little cash to help working people for a measly couple of months. But only if you let us wreck the climate forever!”

The Keystone XL pipeline, you’ll recall, would tap a vast Canadian reserve of dirty tar-sands-derived oil and pump that crude from Alberta to the Gulf of Mexico, imperiling the Great Plains’ fragile Ogallala aquifer and quite probably pushing the global carbon needle permanently into the red. Last month, President Obama postponed approval of the pipeline for a year, after protesters ringed the White House and reporters dug up evidence that the State Department’s process for approving the pipeline was hopelessly compromised by conflicts of interest.

Obama’s pipeline postponement incensed Republicans. This past week, they made it clear that they intended to tie up the entire package of year-end budget bills along with the payroll tax-cut extension unless they got their way. President Obama, in turn, declared that he’d veto any spending bill that tried to force him to approve Keystone XL. The bill we ended up with Saturday morning requires the president to rule on Keystone within two months rather than waiting a year; it forces him to come down for or against it during the middle of an election year.

So why is the right so worked up over this pipeline? As soon as the president decided to delay approval of Keystone XL, Republicans in Congress began insisting that the move was a job-killing sop to “extreme environmentalist groups.” Never mind that the coalition opposing Keystone is a broad-based green alliance that includes bomb-throwing outfits like the Sierra Club and the National Wildlife Federation, as well as both Republicans and Democrats in states like Nebraska threatened by the pipeline’s route. And never mind that pipeline builder TransCanada’s estimate that the project will create 20,000 new jobs has been widely debunked: The only independent study has instead concluded that the pipeline will leave us with perhaps 50 permanent new jobs after a few thousand temporary construction positions evaporate.

You see, Republican intransigence on the Keystone pipeline doesn’t really have to do with disagreements over how to create jobs or assessments of environmental impact. And while the cynical among us will argue that the Republican energy lobby is simply doing the bidding of its corporate contributors, I think the explanation is even cruder than that.

To understand why the pipeline has become the GOP’s line in the tar sand, you have to fathom the nasty logic of alpha-male political messaging in the age of Fox News. You have to grasp what Josh Marshall calls “the Republicans’ bitch-slap theory of electoral politics” — an ugly name for an ugly tactic. Marshall’s idea — originally formulated during 2004′s Bush vs. Kerry campaign — is that Republican campaign moves often aim to expose opponents as weak by, in effect, slapping them to see whether they’ll slap back. A failure to respond exposes you as a weakling; if you won’t defend yourself, how will you defend the nation?

Here’s how the bitch-slap theory relates to Keystone XL. Obama’s pipeline delay represented a rare event in our public life: Street protests led to actual policy change. The president’s reversal was, in fact, the one and only signal achievement progressives could point to in an otherwise dismal year that featured, among many other disappointments, Obama’s cave-in on tightening smog rules. It was a win for the planet and for a mass popular movement — and therefore it could not stand. The impertinence had to be met with a slap. Otherwise, who knows what demands protesters might start making next?

If you understand the psychology that motivates the right’s obsession with winning the pipeline battle, you also understand how much more important it is for Obama not to back down now. If he approves Keystone XL, he’s signaling to his political opponents that their tactics work. He’s inviting more government-shutdown crises and battles over smart fixes for the economy every time he tries to make progress on the issues his own supporters care about.

Today, Beltway insiders are betting that the president will stick to his guns. He’s already declared that 60 days isn’t enough time to review the pipeline; he will simply kill the whole project.

Sure, doing so will open Obama to a campaign-year’s worth of attacks as a job-killing green monster. But giving in to the GOP’s power-trip head games would not only be an environmental disaster, it would cripple him politically, too. Republicans want to cow the protesters and humble the president. Obama can and should slap back.

UPDATE, Monday Dec. 19: When I wrote this piece on Saturday everyone figured that the Senate’s bipartisan compromise package was a done deal. But done became undone over the next day, as Tea Party Republicans in the House decided they hadn’t gotten what they wanted. How this Kabuki drama plays out over the next few days is anyone’s guess. But keep an eye out for the underlying dynamic: The GOP will continue to try to show the president, and the country, who is boss.