By Dan Merica CNN

LOUISVILLE, Kentucky (CNN) -- Vice President Mike Pence, armed with the Republican bill to overhaul the health care system, put subtle but direct pressure Saturday on Republicans thinking about bucking President Donald Trump's administration and their leadership on Capitol Hill over the legislation.

Pence cast the current debate over health care as the best chance Republicans have to repeal and replace Obamacare, President Barack Obama's sweeping 2010 health care law, and said the administration needs all Republicans to be with them in this effort.

"For us to seize this opportunity to repeal and replace Obamacare once and for all, we need every Republican in Congress, and we are counting on Kentucky," Pence said. "President Trump and I know, at the end of the day, after a good a vigorous debate, we know Kentucky will be there, and we will repeal and replace Obamacare once and for all."

The comment was a not-so-subtle reminder to Republicans such as Kentucky Sen. Rand Paul, who has been openly critical of the proposed bill. Pence, speaking at Trane Parts and Distribution Center in northern Kentucky, specifically called out Republican lawmakers who stood with the administration, including Senate Majority Leader Mitch McConnell, also of Kentucky. Pence did not mention Paul.

When asked whether the event was meant as a challenge to Paul, a Pence aide demurred, saying it was no different than the vice president's other events.

"(Pence) will talk about the efforts that are underway to bring people together," the aide said about the vice president's work to win over conservatives. "I think he uses his relationships, and he obviously has longstanding relationships with folks. He understands the legislative process, so he views that as an opportunity to help work on the President's agenda and ushering it through Congress."

Kelsey Cooper, state communications director for Paul, said Paul "is glad to have Vice President Pence in Kentucky today to address healthcare reform, and looks forward to continuing to work with the administration and Congress for a real repeal of Obamacare and replace it with conservative market-based solutions that will bring down prices and give families more choices."

Trump, Pence and their administration have stood fully behind the Republican health care plan despite concerns raised by conservative lawmakers. The GOP proposal has not enjoyed a smooth rollout, but White House aides hope Pence will be able to argue confidently why repealing and replacing Obamacare is best done with this proposal.

The event is a continuation of Pence's health care road show, which has included Missouri, Wisconsin and Ohio. But unlike past events, this time the vice president came armed with a health care plan to sell.

Before addressing a small audience the Trane Parts and Distribution Center in Northern Kentucky, Pence headlined a roundtable discussion with business leaders from the area, where he fielded questions about how the health care law could impact their businesses.

"Most importantly of all, the top priority the President gave us: to work with members of Congress and make sure that the Obamacare nightmare is about to end," Pence said before laying out the issues he said he believes Obamacare caused, including rising premium costs and counties where only one insurer is left offering coverage.

"Folks, this can't continue," he said. "And I promise you, it won't."

Not all Republican are fully on board, though, including Republican Kentucky Gov. Matt Bevin, who attended Saturday's event with Pence.

Speaking with reporters on Friday, Bevin aligned himself with Paul in a subtle knock on the administration's plan.

"Sen. 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 later said he was looking forward to the conversation, but the symbolism was already clear: The Trump administration's health care proposal is controversial enough among some conservatives that even the people appearing with the vice president to sell the bill are expressing skepticism about it.

"Of course there is disagreement as to what we should do with it," Bevin said Saturday. "This is America. Americans have opinions. There is a catastrophe that has been hoisted upon the American people, known as the Affordable Care Act. It has been anything but."

Conservatives were not the only critics following Pence to the Bluegrass State.

Several Democratic groups, including Save My Care, Indivisible and Black Lives Matter, protested Pence's visit, saying they would "stand against Republicans' bill to take away health care from millions."

The protest is part of the Save My Care Bus Tour, a two-month trip aimed at galvanizing support against the Republican health care plan.

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