ROCKVILLE, Md.—Donald Trump is poised to sweep five states’ Republican primaries on the Eastern Seaboard on Tuesday, but his rivals are already looking ahead to next week’s contest in Indiana, which may be their last chance to keep Mr. Trump from clinching the party’s presidential nomination.

Polls have shown Mr. Trump leading in Indiana, which votes on May 3. But Sen. Ted Cruz now might have a better shot at beating Mr. Trump in the state, which has 57 delegates, because the Texas senator struck a deal on Sunday with John...