HOUSTON — After months squaring off against Senator Marco Rubio of Florida, presuming him to be the chief obstacle to a one-on-one showdown with Donald J. Trump, Senator Ted Cruz on Wednesday emerged from the latest Republican primaries with a new foe who was actually there all along: Gov. John Kasich of Ohio.

The transition seemed a bit jarring for all involved. The men had scarcely said a cross word about each other before Tuesday night’s contests.

There had been little need. While Mr. Cruz, of Texas, has moved to consolidate support among evangelical and Tea Party voters, Mr. Kasich has made a play for party moderates, outlasting establishment rivals like Jeb Bush, Chris Christie and Mr. Rubio, who dropped out Tuesday after losing his home state.

Now, it seems, Mr. Cruz and Mr. Kasich will get to know each other a bit better. And their opening gambits were to argue that the other has no chance of becoming president .