Speaking with reporters Friday, Bevin aligned himself with Sen. Rand Paul, the Kentucky Republican who has been a fierce critic of the health care bill.
"Senator Paul has ideas of things he thinks need to be a lot stronger," Bevin said. "He's not as impressed with what has currently been offered as some who have currently offered it. Truth be told, I'm not either, so I'm with him. I think there are things that need to be done."
Bevin added: "The system is broken. It has been broken for some time. It's quickly becoming insolvent. The beautiful thing is, nobody has the solution yet. It's still a work in progress."
Bevin later looked to clear up his comments, saying in a statement that he looks forward to a "frank and detailed discussion" of the legislation.
"It is healthy and appropriate that disparate ideas are voiced at this stage, and I am grateful to President Trump for recognizing and encouraging this," Bevin said. He added that he is confident the final plan will improve health outcomes, be financially sustainable and help states to be innovative health care providers.
"Failure is not an option," he said.
A number of conservative lawmakers and policy groups have come out against the proposed health care plan that the White House is hoping to usher through Congress. Some have even said the plan is only a slightly scaled back version of the Affordable Care Act, President Barack Obama's 2010 law that came to be known as Obamacare.
An Pence aide dismissed the idea that Bevin was standing against the bill, instead arguing that the Kentucky Republican will play a constructive role in what eventually goes to the House floor.
"I think we are all working towards the same thing, and the vice president has been very upfront from day one that governors are going to play a big role in the new health care model as it moves forward," the aide said. "So we want to hear ideas from governors and hear what is impacting them."
In his conversation with reporters, Bevin went on to say he plans to tell Pence that he supports the effort to fix issues that conservatives have raised about the plan.
"Ultimately the solution is going to be giving power and authority back to the states, letting states take care of their own health care needs within their own population, and that is ultimately where it's going," Bevin said.
The comments could make Saturday morning's event at Trane Parts and Distribution Center in Louisville slightly more awkward than it would have been.
Pence and Bevin will both take part in a discussion with business owners before the vice president gives a speech. They will field questions and take suggestions from the business leaders, an aide said.
"(Pence) will explain the plan and talk about the efforts that are underway to bring people together," the aide said.
This will be Pence's fourth event to talk about health care. He has previously traveled to Missouri, Wisconsin and Ohio to stump for an Obamacare replacement.
On Friday, Pence met with the leaders from a number of top conservative groups who have come out against the proposed health care bill, where an aide said he solicited ideas and listened to concerns.