The former presidential candidate said Medicaid covers 700,000 people in his state, a third of whom have mental illness or drug addictions and a quarter of whom have chronic diseases -- people who Kasich said would be hurt by the proposed changes in the bill.
Kasich cited how the bill would limit Medicaid expansion by 2020, which he said would create problems because of the way people cycle off of Medicaid coverage -- and never to get back on.
"I don't have a problem trying to move the Medicaid expansion, which gives an enhanced match from the federal government, to a more traditional match, but you can't do that overnight," he said.
Kasich also said the bill would require certain people to buy insurance policies on the state exchanges, which come with pricey premiums and deductibles, rendering coverage unaffordable for many of those coming off Medicaid. The tax credit provided under the GOP would not be enough to offset the higher costs, Kasich said.
"How do we think that the mentally ill have the ability to pay the deductible on an insurance policy that they have that they can buy for $3,000?" Kasich said, adding that people whose coverage he says would suffer under the bill will be "living in the emergency rooms again."
The Congressional Budget Office's original score of the bill in March stated the plan would cut $880 billion
from Medicaid over 10 years.
However, Health and Human Services Secretary Tom Price refuted the CBO's estimate of cuts earlier in the show and, when pressed repeatedly by CNN's Jake Tapper on whether the projected cuts would translate into millions of people losing coverage, said "absolutely not."
"Remember that there are no cuts to the Medicaid program; there's increases in spending, but what we're doing is apportioning it in a way that allows the states more flexibility to cover their Medicaid and care for their Medicaid population," Price said.
"We believe strongly that the Medicaid population will be cared for in a better way under our program because it will be more responsive to them," Price said.
However, the cuts would put pressure on the states to make up for federal funding shortfalls under the GOP bill, which has a number of governors wary that the lack of funds could lead to them to limit benefits, reduce eligibility or cut provider payments.
"I think the fundamental issue here are the resources," Kasich said. "I don't want to give you exactly the numbers, but it's about half the resources in this bill that were in Obamacare. Now, I can tell you we can do with less resources, but you can't do it overnight and you can't give people a $3,000 or 4,000 health insurance policy. You know where they're going to be? They're going to be living in the emergency rooms again."
"This was not great, and it's going to go to the Senate, and I hope and pray that they write a bigger bill," Kasich said.
On ABC's "This Week with George Stephanopoulos" moderate Republican Sen. Susan Collins of Maine addressed concerns about the bill, saying she hoped it would eventually expand coverage for those still not covered under Obamacare.
"The Senate is starting from scratch," Collins said. "We're going to draft our own bill. And I'm convinced that we're going to take the time to do it right."
White House chief of staff Reince Priebus told Fox News' Chris Wallace on Sunday that he expected the Senate to make any improvements to the House bill and bring it to a House and Senate conference committee.
Asked whether he thought the bill, which was narrowly passed by the House, would become a drag on Republicans in 2018 as Democrats suggest, Priebus said sometimes in life, "you have to do what's right, not what's politically expedient."
"We believe this is going to be a better product," he said. "And by the time the people see that premiums are lower, it's a better service, there are more options and more choices, they're going to reward the Republicans that stood up and said, 'We are not going to see the Obamacare system, which is failing and collapsing, continue any longer. We're going to do something better, and we're going to do our job as legislators to get this thing done.' I think that the Republican Party will be rewarded."