Mike Pence pressed Obama on health care Friday.

STORY HIGHLIGHTS

Washington (CNN) -- As soon as Air Force One touched down in Indiana on Friday, Gov. Mike Pence met President Barack Obama on the tarmac with a plea: Expand the state's access to government-sponsored health insurance.

The catch: Pence wants to do it with a conservative twist.

At least, that's how he's selling his proposal. And his political future could hinge on whether the first-term Republican can convince conservatives that he's not just rebranding Obamacare.

Pence has spent much of his first two years in office trying to strike a bargain on one of the health care law's core components. Indiana will expand Medicaid coverage, Pence says, but only if it's allowed to do it through a tweaked version called the "Healthy Indiana Plan," which also requires users to make small payments into health savings accounts.

He spent five minutes chatting with Obama at the Evansville airport, lobbying to have the Health and Human Services Department green-light Indiana's request, before the president visited a factory in Princeton, Indiana.

"The president and I talked through a number of substantive issues that have arisen in our discussions over the Healthy Indiana Plan," Pence said afterward, "and I appreciated the opportunity to call the matter to his personal attention."

He said he also spoke last night with top Obama adviser Valerie Jarrett, and will meet Monday with HHS Secretary Sylvia Mathews Burwell.

Pence's focus on a health care expansion is at the center of his effort to evolve from a firebrand conservative congressman to an executive with a record of accomplishment ahead of a White House run that many Republicans close to him see as a question of when -- not if.

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Why is this GOP governor talking health care with Obama?