Judge Merrick Garland meets with Sen. Patrick D. Leahy (D-Vt.) on Capitol Hill the day after being nominated to fill the seat of late Supreme Court Justice Antonin Scalia. (J. Lawler Duggan for The Washington Post)

Now that President Obama has nominated Merrick Garland to replace Justice Scalia, the confirmation battle moves to the Senate — and to the public.

The current position of the Senate leadership is that Garland will not even get a hearing. But some Republican senators have already indicated that they would meet with Garland, contrary to the previous “no meetings” policy. How likely would Garland’s confirmation be if the Senate did eventually vote on it?

Many factors will come into play, but one important piece of the puzzle is public opinion. As our research has shown, there is a striking connection between home-state public support for a Supreme Court nominee and how senators vote.

In particular, senators respond to the opinions of their fellow partisans back home. In other words, the votes of Democratic senators are driven by the opinion of their Democratic constituents, and the votes of Republican senators are driven by the opinion of their Republican constituents (controlling for ideology and other well-studied factors).

Why is this important? Consider the graph below, which shows the distribution of public opinion at the state level for 11 recent nominees for which we have suitable data.

The nominees are arranged in chronological order, by the year of their appointment. Nominees in red were appointed by Republican presidents, and nominees in blue were appointed by Democratic presidents. For each nominee, the blue lines show the spread of opinion at the state level among Democrats, the purple line shows the spread of opinion at the state level among Independents, and the red line shows the spread of opinion at the state level among Republicans. The respective dots show the average level of opinion among each type of voter.

For instance, for Chief Justice John G. Roberts Jr., Democratic support ranged from 40 percent of Democratic voters (in New York) to 58 percent (in North Dakota). The average level of support for Roberts among Democrats was 48 percent.

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Until recently, there was actually a lot of overlap among Democrats, independents and Republicans (with the nomination of Robert Bork an exception). Even during the nomination of Clarence Thomas, who overcame a scandal to barely win confirmation, Democrats in nearly every state favored his confirmation.

However, the five nominations before the current one, including the failed nomination of Harriet Miers, have seen substantial polarization — with citizens of the president’s party strongly supporting the president’s nominee, and citizens of the other party strongly opposing the nominee.

This shift has tracked the change in voting breakdowns in the Senate. Whereas President Clinton’s nominations of Ruth Bader Ginsburg and Stephen Breyer were confirmed by near-unanimous margins, the last four nominations have been much closer to party-line votes.

President Obama has nominated Merrick Garland to serve on the Supreme Court. Here is what you need to know about Garland. (Claritza Jimenez,Gillian Brockell/The Washington Post)

In our research, we found that senators vote in line with the preferences of their home state around 75 percent of the time. But they vote in line with their fellow partisans in the electorate around 87 percent of the time. Take a Republican senator. When the median voter in the state says to reject but the median Republican in the state says to confirm, the senator votes to confirm 82 percent of the time.

If you flip that so that the median voter says to confirm, but the median Republican says to reject, the senator votes to reject 73 percent of the time. So a partisan split in opinion can have important consequences for the fate of a politically contentious nominee.

Why does this happen? We think it’s because a senator voting against his or her base faces the prospect of facing a challenger in a primary — and possibly being tossed from office. Indeed, senators don’t have to look very far for examples of this happening.

In 1992, Alan Dixon, a Democratic senator from Illinois, was defeated in the primary by Carol Moseley Braun, who campaigned in large part against Dixon’s vote to confirm Thomas.

And, just four years, ago, Richard Lugar — a six-term senator — was defeated by Richard Mourdock in the Republican primary, after Mourdock campaigned against Lugar’s votes to confirm Justices Sonia Sotomayor and Elena Kagan. Senate Republicans do not want to suffer the same fate when their next election rolls around.

Even before the Garland nomination was announced, public opinion on whether the Senate should consider a nominee this year or leave the seat vacant until the next president takes office split along partisan lines. A poll earlier this month found that 55 percent of registered voters disapproved of the Senate leadership’s decision not to consider a nominee. However, 69 percent of Republicans approved of the decision, while 79 percent of Democrats disapproved of the decision.

This split in public opinion has put Republican senators who are up for reelection this year (such as Rob Portman and Kelly Ayotte) in a tough spot. Much will depend on whether polarization extends to key states. Our work predicts that if enough Republican constituents in key states are on board with the nomination of the relatively moderate Garland, then the senators will follow.

In a surprise move, President Obama has selected appeals court judge Merrick Garland to replace Justice Antonin Scalia. The Post's Jerry Markon explains the possible strategy behind his choice. (Claritza Jimenez,Gillian Brockell/The Washington Post)

Furthermore, if Republicans block the confirmation of Garland, they face the prospect of a Democratic president and a Democratic Senate getting to nominate and confirm a replacement for Scalia. Democratic senators will be listening to Democrats back home. This should lead to a nominee who is more liberal than Garland. Will this possibility be enough to push Republican senators toward confirmation?

The picture should become clearer as polling on Garland’s confirmation emerges. If the GOP constituents of more moderate Republican senators support his confirmation, Garland may have a chance.

If they don’t, his chances may drop from slim to none.

John Kastellec is an assistant professor in the department of politics at Princeton University. Jeffrey Lax and Justin Phillips are associate professors in the department of political science at Columbia University.