WASHINGTON — As Republicans try to move past the furor that Donald J. Trump provoked with his attack on a Mexican-American judge, party leaders are finding themselves in the unpleasant position of asking yet again just how far is too far — and what, if anything, they can do to keep Mr. Trump in check.

Some lawmakers, senior members of the Republican National Committee and delegates to the party’s convention next month in Cleveland acknowledged in interviews this week that another disruptive self-inflicted crisis would force the party to begin seriously looking at ways to deny Mr. Trump the nomination.

So far, discussions of a renewed dump-Trump drive have taken place only among the factions of the party that are openly opposed to Mr. Trump, and they have failed to gain much support.

But Mr. Trump’s suggestion that Judge Gonzalo P. Curiel’s Mexican heritage should disqualify him from hearing a lawsuit against Trump University has reawakened talk of hatching a convention coup — a complicated and nearly impossible measure of last resort that has no precedent in modern Republican politics.