WASHINGTON — A third Democratic senator announced his support on Sunday for President Trump’s Supreme Court pick, Judge Neil M. Gorsuch, though Republicans still face the difficult task of gaining enough Democratic votes to confirm Judge Gorsuch without potentially having to change longstanding Senate practice.

The senator, Joe Donnelly of Indiana, is among a group of 10 Democratic senators who represent states that voted for Mr. Trump and who are up for re-election in 2018. So far, two others — Joe Manchin III of West Virginia and Heidi Heitkamp of North Dakota — have announced their support for Judge Gorsuch.

That leaves Republicans, who hold 52 seats in the Senate, five Democratic votes short of breaking any filibuster mounted by Democrats. If the Republicans do not have enough votes to break a filibuster, they could invoke the so-called nuclear option, allowing them to eliminate the filibuster for Supreme Court nominees and hold a floor vote. Judge Gorsuch could then be confirmed by a simple majority.

Mr. Donnelly said in a statement that he would vote for Judge Gorsuch because “he is a qualified jurist who will base his decision on his understanding of the law and is well respected among his peers.” Mr. Donnelly said he believed that the Senate should keep the 60-vote threshold to end a filibuster of a Supreme Court nominee.