The death of Supreme Court Justice Antonin Scalia today set off a scramble in a deeply polarized Washington over his replacement on the court. Within hours of the announcement of Scalia’s death, Senate Majority Leader Mitch McConnell said a vote should wait for the next president to be elected. He and the Republican majority in the Senate can impose extensive delays on any confirmation vote.

But if Obama is able to get consideration for a nominee, history and common sense suggest that it will be very difficult for him to win approval for judicial candidates with the qualifications and ideological backgrounds of his first two nominees, Sonia Sotomayor and Elena Kagan.

In November 2014, I tried to model how Supreme Court nominees over the past 50 years would fare if their confirmation were up to the current Senate. The model I used was fairly simple and looked at the ideology and qualifications of the nominees as judged by their Segal-Cover score, the party and ideology of each senator as recorded by their DW-Nominate score, and the approval rating of the president.

As you can see from the chart, a liberal titan like Thurgood Marshall probably would not get a majority of votes in the Senate today, though Sotomayor and Kagan would. The problem is that they would fall short of the 60 votes needed to break a very possible Republican filibuster. Indeed, that is one of the biggest problems Obama will have in trying to get any justice confirmed. He may be able to pick up a number of moderate Republicans, especially those facing tough re-election fights, but he’ll need at least 14 Republican votes to get to 60.

That’s assuming he gets a vote on any nominee, because Republicans look like they may try to run out the clock until the end of Obama’s term. Conn Carroll, communications director for Utah Sen. Mike Lee, who is on the Judiciary Committee, tweeted that Obama has a “less than zero” chance of successfully replacing Scalia on the Supreme Court.

The first time a Supreme Court nominee was filibustered was in the months leading up to the 1968 election, when President Lyndon Johnson unsuccessfully tried to elevate Justice Abe Fortas to the position of chief justice. (The nomination was filibustered mainly because of ethical concerns about Fortas.) As the Congressional Research Service found, “many” of the Supreme Court nominees ultimately voted down by the Senate because of opposition to the president were nominated or debated in the last year of a president’s term.

Besides the election, the other big hurdle facing Obama is that Scalia was a conservative cornerstone of the court. Sotomayor and Kagan, by contrast, were replacing two liberal justices. The potential to change the ideological tilt of the court would likely lead to high interest-group opposition from anti-abortion groups among others. Charles M. Cameron and Jonathan P. Kastellec of Princeton University and Jee-Kwang Park of American University have argued that interest groups play a key role in determining whether a nominee is opposed vigorously by a party that does not hold the White House.

If Obama does make a nomination, what type of nominees should he consider? Not surprisingly, the model indicates that more moderate and better-qualified nominees would have an easier time being confirmed. Ruth Bader Ginsburg was very well-qualified, and even though she was a mainstream Democrat, she was nearly unanimously confirmed. My guess is that in the current hyper-polarized Congress, a nominee like her wouldn’t come close to the vote total the model suggests for a well-qualified mainstream Democrat, but she’d stand a chance.

The other option is a candidate like Stephen Breyer who, despite a Segal-Cover score indicating that he wasn’t as qualified as Ginsburg, flew through his confirmation proceedings because he was thought to be more moderate. You might also remember that Anthony Kennedy was confirmed during the 1988 presidential campaign with little opposition. He was seen as much more moderate than Robert Bork, who had previously failed to get through the Senate because of a very conservative record.

But 1988 was a long time ago and a different political era. Obama’s likely to have a tough fight on his hands no matter how well-qualified or moderate his nominee. This will probably be the most contentious Supreme Court nomination since that of Clarence Thomas in 1991.