We know, of course, that the Republican majority in the United States Senate is not going to approve any candidate President Obama nominates to the Supreme Court. With the death of Antonin Scalia, the conservatives have lost their 5-4 majority on the court and whoever is chosen to replace him will tip the balance. The Republicans would far rather take their chances on the coming election and wait it out in the hopes that they’ll be able to appoint another conservative in January 2017.

Of course, Twitter is abuzz today with all of the potential “blue state” Republicans and halfway reasonable GOP Senators who might be persuaded to join Democrats in approving a nominee, but this is a fantasy. These theories all leave out the facts that there will never be enough aisle-crossers to break a filibuster (which would require any nominee to get 14 Republican votes, not four), or that Senate Majority Leader Mitch McConnell (R-Kentucky) does not even have to call a vote.

So clearly this isn’t going to happen. The next president and the next Senate will select Scalia’s replacement, period.

With this understanding, President Obama and the Democrats should be thinking about how to gain the maximum political benefit from Republican intransigence. And the way to do that is to nominate Senator Elizabeth Warren (D-Massachusetts) to fill the vacancy.

There is no question of Warren’s qualifications. The former Harvard Law professor has impeccable credentials, so Republicans could not claim she is unqualified. It would therefore become clear, if it wasn’t already, that they were blocking her for strictly political reasons, and this would diminish their standing with the few true swing voters.

But there are greater political benefits to be had. First, a Warren nomination would provide a jolt of energy to progressives who adore her, which could be crucial in terms of base turnout in the upcoming election. Secondly, nominating a fourth woman to the court would reiterate that Democrats are the party of equality.

Both Hillary Clinton and Bernie Sanders could take this ball and run with it, hammering the Republicans for blocking an eminently qualified (progressive, female) nominee. Meanwhile, the president can also exploit this situation to hammer the Republicans every day.

There is no need to worry about who would replace Warren in the Senate because, as noted above, there is no chance in hell the Republicans will approve her (or anybody) between now and the next presidential inauguration. So if the Republicans want to play hardball, the Democrats have a great way to win the war by losing the battle.