There's some historical precedent for Republicans to do just that, even though Americans say 2-to-1 in a recent Washington Post-ABC News poll the Senate should hold hearings on Obama's nominee.
A hazy rule dating back decades that congressional experts say is really more of a tradition suggests senators can oppose some of the president's judicial nominations in the months before a presidential election.
It's known as the "Thurmond Rule," for reasons we'll get into, but there is widespread disagreement on what it even means and when it can be invoked.
"It's not a rule," said Russell Wheeler, a judicial expert with the Brookings Institution. "It's just sort of a pie-in-the-sky flexibility that both parties try to disown when it's convenient for them and try to say it means something when it's not."
Whether rule or tradition, it pops up throughout history in times like these, when a high-stakes judicial nomination collides with a presidential election.
But Wheeler and other congressional experts think the rule is less in-play now than in the past. Republicans have control of the Senate and can simply sit on the nomination if they want — no matter how much the other side cries foul.
To do that, Republicans are largely skipping over the validity of a somewhat-arcane parliamentary tradition and making the argument that it's not fair to consider a life-time judicial nominee by a lame-duck president before such a pivotal presidential election. "Let the people decide" is what they're saying.
Hours after Scalia died, Senate Majority Leader Mitch McConnell (R-Ky.) appeared to say just that in a statement. "The American people should have a voice in the selection of their next Supreme Court Justice," his statement read. "Therefore, this vacancy should not be filled until we have a new President.” He has since doubled down on it, including in a joint op-ed in The Washington Post with Sen. Chuck Grassley (R-Iowa), the chair of the Senate panel that would review Garland's nomination. To vote on a nominee now would be robbing voters of the chance to replace Scalia, they said.
Senate Minority Leader Harry Reid (D-Nev.) fired back in a statement that spending an entire year without considering Obama's nomination to replace Scalia is unprecedented.
"It would be unprecedented in recent history for the Supreme Court to go a year with a vacant seat," he said. "Failing to fill this vacancy would be a shameful abdication of one of the Senate's most essential Constitutional responsibilities."
Reid's office circulated some recent stats noting that, since the Ford administration circa 1975, it has taken on average two months between a judicial nomination to the final Senate vote. Today, it's about 75 to 90 days on average from the time of a vacancy to appointment on the Supreme Court.
Reid is banking on historical precedent that the Senate has typically stopped considering judicial nominations the summer before a presidential election, after each party has nominated its nominee. In other words, the Thurmond Rule hasn't typically extended to an entire year.
But the rule is really a guideline that is often pulled out by both parties whenever is expedient (Republicans like to point to Vice President Joe Biden's 1992 comments on this as Exhibit A). Here's the background:
In the summer of 1968, Sen. Strom Thurmond (R-S.C.) opposed President Lyndon B. Johnson's choice of then-Justice Abe Fortas to the top spot on the Supreme Court as chief justice. (In the Senate, one senator can block just about anything.)
Thurmond's rationale for blocking Fortas's promotion was both parliamentary and political. Johnson, who wasn't running for reelection, was a lame duck. His proposed promotion for a Supreme Court justice came just six months or so before the presidential election that Thurmond's party had a good chance to win.
Thanks to Thurmond's opposition, Fortas never got the top job. And opposing judicial nominations in the summer before an election year became known as the Thurmond Rule. The judicial battle of the summer of 1968 rears up in the Senate from time to time, especially recently.
In 2004, Senate Democrats, then in the minority, debated dusting off the then-dormant "rule" to block President George W. Bush's nominees before the election. At the time, some senators probed by reporters didn't even know what the rule referred to.
The Hill reported at the time: "Sen. Trent Lott (R-Miss.) could only come up with a guess at what it might mean: for a senator to stay in the Senate 'until you can’t walk.'”
In 2008, as Bush was trying to get judicial nominees through a Democratic-controlled Senate, then-minority leader McConnell said, "There is no Thurmond Rule."
And in June 2012, McConnell said his party would block some of Obama's judicial nominees to the circuit court until September.
Now eight months before this presidential election, McConnell seems set on blocking Obama's nominee to fill Scalia's seat. And whether he invokes the Thurmond Rule or not, he'll probably be able to do it.