The most important Senate committee vote Thursday on a top-tier White House nomination was neither the party-line ballot advancing Thomas E. Perez one step away from becoming Labor secretary, nor the parallel 10-8 vote advancing the choice of Gina McCarthy as EPA chief to the Senate floor.

The day’s most consequential roll call was at Senate Judiciary, where all eight Republicans joined the 10 Democrats in endorsing Sri Srinivasan for a seat on the D.C. Circuit Court of Appeals.

Such unanimity is an extraordinary and unmistakable sign that GOP conservatives are making a tactical retreat in the judicial wars — one that may influence the filling of a future seat on the Supreme Court.

Even as those Republicans contemplate filibusters designed to stop Perez or McCarthy from taking seats in the president’s Cabinet — where they could shape policy for three and a half years at most — they’re preparing to concede their side’s clear ideological advantage at the country’s second-most-important federal courthouse. And they look ready confirm someone who might hold sway over social and regulatory policy for three decades or more.

A lopsided confirmation vote by the full Senate, which now looks inevitable and could come within a month, would boost the odds that President Barack Obama turns to Srinivasan should a vacancy on the top court come open in the next three years. Four of the current high-court justices stepped up from the D.C. Circuit, which has unusual influence over federal policy because it hears constitutional appeals of most decisions involving government agencies and departments based in the capital.

On paper, there’s no apparent reason for senators to deny Srinivasan whatever promotion he’s up for. He’s spent the past two years as the principal deputy solicitor general, the president’s No. 2 advocate at the Supreme Court. He’s argued there two dozen times, most recently for the administration’s point of view in the Defense of Marriage Act case.

But Srinivasan also spent five years working in President George W. Bush’s solicitor general’s office, after clerkships for Justice Sandra Day O’Connor and a conservative appeals judge in Virginia. In between, he was a partner specializing in federal appellate litigation at a top-flight firm, O’Melveny & Myers.

That gold-plated résumé means he’s spent virtually his entire career litigating on behalf of others, not espousing his own views. And, in the modern era of intense combing through every utterance of every appeals court nominee, the lack of a paper trail is working to his benefit. Conservatives have found almost nothing in his record to point at with concern, although neither have liberals found much tangible reason to believe he’d be on their side.

Srinivasan is about to become the first federal appeals judge of South Asian heritage and, at 46, the youngest judge on the D.C. Circuit. Of more consequence, he’ll be the first newcomer to that court in seven years. Since 2006, the number of vacant seats has grown to four. Of the seven full-timers on the bench, four were nominated by Republicans and three by Democrats, so Srinivasan will make it an even split.

That simple math helps explain why all those seats have stayed vacant since long before the election — and why that situation is about to change, although only a little bit.

Obama has made just two nominations for the D.C. Circuit so far. And he spent considerable effort promoting his other choice, former New York Solicitor General Caitlin J. Halligan, giving up only after successful filibusters in both 2011 and 2013 by Republicans complaining she was an outside-the-mainstream activist liberal.

Those senators have found no plausible rationale for opposing Srinivasan the same way, which would guarantee renewed Democratic threats to invoke the “nuclear option” of changing Senate rules to ward off any future judicial nominee kill-with-delay campaigns

The only politically safe Republican option is to gamble that Srinivasan’s current ideological mysteriousness will evolve into centrism on the bench, that no Supreme Court seat opens up  anytime soon — and that they can prevent any of the remaining three D.C. Circuit vacancies from getting filled while Obama’s in office.

The president knows this is the GOP fallback position, and he’s already readying his tactical response: a roster of three D.C. Circuit choices to be nominated in coming weeks as a slate — challenging the Senate, in effect, to embrace at least one of them because surely they can’t all be activist leftists.

The Republicans know this is coming and have their counter-programming planned out: There’s no need to seat anyone else, they’ll insist, because the court’s caseload is not big enough to justify the eight judges on the job.

The Srinivasan confirmation will shift the judicial wars into something more like a chess match. The stakes will be just as high, and in some ways, it might be more fun to watch.