To some Republicans, it was a week that amounted to a series of Hail Mary passes by a candidate running out of time. “Cruz is so desperate that he is throwing everything—including the kitchen sink and the Indiana Old Oaken Bucket—at Trump,” said Rick Hohlt, a GOP fundraiser who is moving toward supporting Mr. Trump, referring to a college football trophy.

Mr. Cruz acknowledges that his presidential prospects will all but collapse if Mr. Trump sweeps Indiana. While the front-runner can’t secure the 1,237 delegates needed to clinch the nomination until the last day of primary balloting on June 7, it is hard to see how he can be stopped if anti-Trump forces don’t prevail in Indiana.

“Make no mistake, Indiana is absolutely pivotal,” Mr. Cruz said in a fundraising email. “If Trump wins all the delegates in Indiana, his nomination could be all but determined.”

A big obstacle to stopping Mr. Trump, however, is that many Republicans are loath to throw their weight behind Mr. Cruz, who has earned GOP wrath by trashing the party leadership in Congress.