One such idea, according to a GOP source familiar with discussions, would be a so-called "split the map" strategy for the remaining GOP contests. Ohio Gov. John Kasich's campaign would focus on eastern states where his brand of Republicanism is most salient, and Texas Sen. Ted Cruz would put his efforts in western states where he tends to do better.
Behind this strategy is the reality that Donald Trump is so far ahead with GOP delegates that the best way to keep him from getting close to the 1,237 needed for the nomination is to have one opponent in each contest.
Because neither Kasich nor Cruz intends to drop out, the idea would be for Kasich to put his resources and time in states like New York, Delaware, Maryland, Pennsylvania and Rhode Island, which have primaries at the end of April. Cruz would keep his focus on states like Arizona and Utah this coming Tuesday and then Nebraska, Oregon and South Dakota in the months to come.
When asked about the idea in an interview that aired Sunday on CNN's "State of the Union," Kasich said he is "not thinking that way" at this point, but that "we always talk."
But he added: "You gotta understand that this is sort of a mission for all of us, and it's not just me, it's the team."
He also said he thinks he can win all over the country.
"I'm thinking that we're getting momentum and I can go East and I can go West. You know, think about California and me, OK, you know, I've got positions that unify people," Kasich said.
A senior Cruz official told CNN the campaign had heard about the "split the map" strategy but dismissed it as not viable.
But the concept underscores the panic among many Republicans at the prospect of Trump arriving at the convention in July with far more delegates than anyone else, making it harder to decide on someone else as the GOP nominee.
'Everybody needs to take a little chill pill'
Kasich needs a contested convention to have any shot at the nomination at this point, since he has no mathematical path before that. But he says he was at the last contested GOP convention in 1976 and it worked out well. Then, Gerald Ford was nominated to a full term, after a strong challenge from then-California Gov. Ronald Reagan. Kansas Sen. Bob Dole was nominated as his vice president.
"I don't know why everybody's so panicked about this. Everybody needs to take a little chill pill, to tell you the truth," Kasich said on "State of the Union."
But Kasich made it clear he is banking on the idea that come convention time, GOP delegates will realize that he is the only one left in the race who can win in November.
"I think we're going to go to a convention -- which is really an extension of the political process -- and when we get there, the delegates are going to think about two things: No. 1, who can win in the fall? And I was glad to hear Lindsey (Graham) say 'Kasich's the best general election candidate' because I don't think the other two can win," Kasich said. "And secondly -- now this is a crazy idea -- who actually could be president of the United States and do a good job? When the delegates think about that, I think we will do very well and we will go to the convention with momentum."
Kasich once again dismissed the notion that some in the Cruz camp are pushing that the Ohio governor should drop out to stop Trump, noting that that's what Republicans wanted a few weeks ago to clear the way for Marco Rubio.
"They were all gonna get behind Rubio, right? And he's gone. I'm still here. You know what would've happened had I dropped out? You know who would've won Ohio? I won Ohio. I didn't win Ohio in any calculation. I won Ohio because of my message and my record, and guess what? As a result of that, Donald Trump is not going to go to the convention with enough delegates," Kasich said.
The Ohio Republican continued to push back on Trump's suggestion that a contested convention that didn't end with Trump as the nominee would result in rioting in the streets.
"I don't think that kind of language is appropriate, to talk about violence and rioting. I know you don't. It's inappropriate. I'll also tell you the threats on Donald Trump's family are outrageous. They have no right to be threatening his family," Kasich said. "So why doesn't everyone just realize we're better in America when we're together and we're unified. And if you go to a convention and you lose, be a big enough person to say, 'I gave it my best and I didn't win.' That's what I would say if I didn't."