Haley Barbour, the former Mississippi governor and Republican National Committee chairman, said any rush to get behind Cruz -- or any single candidate for that matter -- would short-change the process.
"I am not of a mind that people ought to be for somebody they're not for because of some strategy that somebody's dreamed up," Barbour said in an interview. "I still think there's plenty of time to be for who you think would make the best president."
Romney announced Friday he would vote for Cruz in the Utah caucuses, saying in a Facebook post that the Texas senator was the only candidate remaining that could stop Trump. The vote was not an endorsement.
Instead, Romney said backing Cruz was the best way to deny Trump the requisite delegates needed to secure the nomination before the Republican convention. Should that happen, it would force an open convention -- and an opportunity to deny Trump the nomination, even if he held the most delegates.
Romney's position is one that is gaining momentum among party leaders, but directly undercuts the third candidate in the race: Ohio Gov. John Kasich, someone Romney campaigned with just five days prior.
"A vote for Governor Kasich in future contests makes it extremely likely that Trumpism would prevail," Romney wrote. Yet Barbour said it's a strategy that is being pursued too soon. Barbour, who has played a role in every Republican primary since 1968, said that while Trump is more likely to win the nomination than anyone else running, the race "is far from over."
Voters should "not feel like they have to be for somebody they ought to be for because of some contrived theory of how an open convention operates," Barbour said.
Still, the Romney announcement raises potential problems for Kasich by putting a bold-faced name -- not to mention its most recent nominee -- behind a strategy that essentially advocates for Kasich's exit from the race. John Weaver, Kasich's chief strategist, fired back with a statement, saying, "It is unfortunate to see that Mitt Romney is getting bad political advice."
Kasich kept his campaign alive with a sizable victory over Trump in his home state of Ohio -- his first state victory of the race. He trails Trump heavily in delegates, however, leading Romney to push for consolidation behind Cruz.
Cruz, on Friday in Arizona, said Kasich had "not a good reason" to stay in the race. On Saturday, in Utah, he questioned Kasich's motives.
"What I think is undoubtedly clear is that John Kasich cannot win the nomination," Cruz told reporters. "That it is mathematically impossible for him to win the nomination, that a vote for John Kasich is a vote for Donald Trump. I don't know if John Kasich is perhaps campaigning to be Donald Trump's vice president."
Kasich, in an interview with MSNBC on Friday, said there was "no chance" he would be Trump's vice president. But he and his advisers are honest about their path forward to the nomination: an open convention.
Mathematically, Kasich has little to no chance of reaching the 1,237 delegates needed to secure the nomination before the convention. But he has said he's targeting an open convention, one that would be held in his home state of Ohio. His team hopes to pull in enough delegates in future contests on the East Coast and in California to best position him for exactly that.