Both campaigns have their eye on a small group of delegates at the convention known as the Rules Committee. Usually a footnote in any party convention, this group of just over 100 delegates will have an outsized influence if the race continues to move toward a contested convention.
That's because the 112 individuals representing all states and territories will be the ones to decide the rules for the entire convention -- including what bar to set for candidates to be eligible to be voted on.
There is a rule on the books as of now, referred to as Rule 40, that requires any candidate to get a majority of delegates in at least eight states to appear on the nominating ballot at the convention. Kasich has only won one state: his home state of Ohio.
That rule can easily be changed by the Rules Committee at this year's convention -- but both Trump and Cruz have spoken in favor of the rule, and Trump adviser Barry Bennett expects the two men to largely control the Rules Committee.
"We're going to have a majority on that, and if (Cruz) doesn't want Rule 40 be changed, then it's not going to be changed," Bennett told CNN. "So there's no way for John Kasich or Mitt Romney or whoever it is to even get nominated, it's going to be Donald Trump or Ted Cruz."
Cruz has clearly spoken in favor of preserving the rule.
"There is a real possibility that nobody gets to 1,237," Cruz told conservative radio host Hugh Hewitt last week, referring to the number of delegates needed to clinch the nomination outright.
"If that's the case, we should operate under the rules that existed when this whole process started. And those rules say that in order to be on the ballot, you have to have won eight states. Only two of us will meet that threshold -- me and Donald Trump. Those will be the two names on the ballot," Cruz said.
On Monday, he added that he expects his supporters and Trump's supporters to preserve it.
"If there's a contested convention, 80% of the delegates are gonna be Cruz delegates or Trump delegates," Cruz told reporters in Wisconsin. "Both Donald and I have been very clear, we shouldn't be changing the rules because Washington is unhappy with how the people are voting."
And Trump has echoed it as well, saying Kasich shouldn't be able to continue siphoning off votes from the front-runner.
"Kasich shouldn't be allowed to run. Honestly, Kasich should not be allowed to run," Trump told reporters Sunday while visiting a diner in Milwaukee. "Kasich shouldn't be allowed to continue, and the RNC (Republican National Committee) shouldn't allow him to continue."
Kasich responded on Monday.
"Donald Trump said that I need to get out of the race because I'm getting his voters," Kasich said at a New York town hall. "I got news for him, I'm gonna get a heck of a lot of his voters ... because I understand exactly what his voters are worried about."
Choosing the members
The Rules Committee is built of two representatives from each delegation to the convention, in most cases chosen within the delegates from each state. Traditionally, the people chosen to represent each state and territory have been more senior members of each delegation, usually ones familiar with the process and rules of the party.
There is already an all-out effort underway by each campaign to secure as many delegates to the convention in Cleveland in July.
Though the vast majority of delegates are bound by state results on at least one ballot at the convention, if no one gets a majority, about eight in 10 delegates could be free agents to vote for whomever they choose by a third ballot. That has sent operatives scrambling to ensure that the men and women being selected in all 50 states and the territories are favorable to their side.
Trump and Cruz are on the front lines of this effort, with Cruz looking to outmaneuver Trump as a way to make up ground in the overall delegate count, which Trump leads by nearly 300.
One state-level RNC member who spoke on condition of anonymity predicted that many of the delegates chosen for the Rules Committee will be the state party chairs or committeemen and women, as they are senior and informed members of each delegation, and that could bode well for anti-Trump forces in the establishment who fear him as the nominee.
But Cruz has also clashed with the establishment, and it's not clear if those party insiders could open up the rule, which was put in place last election cycle to prevent Ron Paul supporters from making noise at the convention where Mitt Romney was officially nominated.
RNC spokesman Sean Spicer sought to downplay the idea that the rules this year would be unusual, saying they are always set by the needs of the election year.
"The delegates of this, which are largely going to be Cruz and Trump delegates, will sit down, elect members to be on the rules committee. and then craft rules for this convention the way it has always been, since the 1800s," Spicer said on CNN on Monday.
The Cruz campaign insists it is not in cahoots with the Trump campaign. "There is unequivocally, positively no coordination," a Cruz official said.
Cruz's spokesman downplayed the efforts, saying it was up to Kasich to win more states.
"With his impressive string of losses John Kasich has done a pretty good job on his own boxing himself out of the nomination," Ron Nehring told CNN. "John Kasich's problem isn't the rules of the Republican Party, it's that voters aren't buying what he's selling."
Kasich's spokesman Chris Schrimpf called the efforts "devious."
"These are more devious and dishonest tactics by Ted Cruz and Donald Trump. They are misleading voters in a desperate attempt to undermine Gov. Kasich because they are afraid to face him as the race moves East. They know Gov. Kasich will win at the Convention because he is the only Republican who can defeat Hillary Clinton," Schrimpf said.
MSNBC first reported