President Obama will have one last chance to force Judge Merrick Garland onto the U.S. Supreme Court on Tuesday — but it’s a legal gamble and one that has so many pitfalls that even those who say he could get away with it believe it isn’t worth the fight.

Mr. Obama’s moment will come just before noon, in the five minutes that the Senate gavels the 114th Congress out of session and the time the 115th Congress begins.

In those few moments the Senate will go into what’s known as an “intersession recess,” creating one golden moment when the president could test his recess-appointment powers by sending Judge Garland to the high court.

A smattering of activists has asked him to give it a try, but Mr. Obama has given no indication that he’s thinking about it. The White House didn’t respond to a request for comment for this story.

The move would be a legal gamble under the high court’s last ruling in 2014 on recess appointments. That 9-0 decision overturned a handful of Mr. Obama’s early 2012 picks, saying the Senate was actually in session when the president acted, so he couldn’t use his powers.

That ruling also said, however, that there’s a difference between appointments made during the annual yearlong session of Congress, dubbed “intrasession,” which Mr. Obama used in 2012, and picks made at the end of the year, after Congress adjourns, which are known as “intersession.”