Former candidate Governor John Kasich speaks at the White House in Washington Thomson Reuters The road to repealing and replacing the Affordable Care Act, the law better known as Obamacare, has been rocky for Republicans. And Ohio Gov. John Kasich's approach going forward could signal which path the party takes.

While the House of Representatives passed the American Health Care Act, their plan to overhaul the healthcare system, in early May, the legislation was unpopular with the public. And Senate Republicans have since indicated that they are writing their own version of the bill.

The House bill, which was altered from an initial version to gain the support of the hardline conservative House Freedom Caucus, has no chance of passing the far more moderate Senate, where Republicans operate with a slim 52-to-48 majority.

One of the most contentious aspects of the AHCA is its proposed rollback of Medicaid, the government-run health program that provides insurance primarily to pregnant women, single mothers, people with disabilities, and seniors with low incomes.

The AHCA would end the government's commitment to funding the expansion to Medicaid established by Obamacare, which extended eligibility for the program to include any adult living under 138% of the federal poverty level.

Thirty-two states and the District of Columbia have chosen to participate, leading to more than 11 million new people nationwide gaining coverage, a number that continues to grow.

The Medicaid expansion has been extremely popular, both with the public and elected officials on both sides of the aisle. While 16 Republican governors have come out in favor of the expansion, Ohio Gov. John Kasich has been the most outspoken. It has made him something of a kingmaker when it comes to healthcare reform in Washington.

Senate Majority Leader Mitch McConnell can only afford to lose two votes in order to pass a Senate bill. Four Republican senators — Sens. Rob Portman, Shelley Moore Capito, Cory Gardner, and Lisa Murkowski — all came out against the AHCA in March due to its handling of the Medicaid expansion.

Kasich's stance on the bill could signal or even dictate where Portman, a senator from Ohio, or the other senators in the group stand.

Nowhere was the importance of Kasich's opinion more apparent than when the New York Times reported Tuesday that Kasich had said he would accept "phasing down the enhanced federal payments" provided by the Medicaid expansion, so long as such a phaseout provided more funds than the AHCA and more flexibility in how to administer the program.

"I don’t have a problem with phasing down the enhanced federal payments," Kasich told the Times. "But it can’t be done overnight, and it has to be done with the resources and the flexibility that are needed so people don’t get left behind. You just can’t be cutting off coverage for people."

Kasich said, according to the Times, that a seven-year phaseout of the Medicaid expansion — which Senate Republicans, including Portman, are reportedly discussing in closed-door meetings — would be acceptable if states were given more autonomy over the program. The AHCA, the House's bill, would end funding the expansion in 2020, among other sweeping changes.

Kasich's statements would seem to suggest that Senate Republicans could be close to a workable compromise on Medicaid, and therefore a healthcare bill as a whole.

But several hours after the Times' story published, Kasich published a cryptic statement:

John Weaver, a Kasich strategist, then said on Twitter that Kasich does not support any "CURRENT plan" in either the Senate or the House, which he said included the seven-year phaseout.

Kasich and Weaver's quick response to the Times story suggests the Ohio governor is well aware how much his "rubber stamp" could mean to Senate Republicans stuck in a difficult and increasingly unpopular bid to pass healthcare reform.

The Senate GOP must forge a compromise bill that will not only make it out of the upper chamber, but gain enough support among the more conservative elements of the House to pass there. Additionally, procedural rules in the Senate prevent major overhauls to Obamacare, as GOP Sens. Chuck Grassley and Joni Ernst acknowledged in May.