Gov. Charlie Baker, the moderate Republican heralded as the most popular chief executive in the nation, takes his act of intensive bipartisanship to Capitol Hill Thursday. As one of five governors set to testify before a Senate health care panel, Baker will pitch saving the federal government's investment in Medicaid to senators who have largely abandoned anything resembling bipartisanship.

At stake is the Massachusetts health care system and the nation-leading medical industry it supports. After an ultimately failed attempt to repeal and replace the Affordable Care Act, Republicans in the Senate are working on their next stab at changing how the federal government provided health services for the poor and aged. Baker estimates repealing the ACA would cost Massachusetts $1 billion in federal dollars.

According to the State House News Service, Baker will urge an extension of at least two years of cost sharing between the state and federal governments.

Local health care experts from the left and right sides of the political spectrum expect Baker to advocate for stability in the health care market going forward.

"I think the sticking point for Gov. Baker here is that there is a lot of federal taxpayer money that has propped up what Massachusetts has done, and that's really where the rub is in this discussion," the Pioneer institute's Joshua Archambault told WGBH News.

Most Washington Republicans, but not enough to polish off a piece of legislation, want to decrease the federal government's involvement in health care. When it comes to health care, Republican Baker has more in common with Senate Democrats and GOP dissidents like Senators John McCain of Arizona and susan Collins of Maine.

Baker, a former state health secretary and insurance executive, should feel comfortable testifying in front of the Senate's Health, Education, Labor and Pensions Committee, said Stonehill College political scientist Peter Ubertaccio.

"I don't think Charlie Baker needs to be worrying about the White House," Ubertaccio said. "This administration is historically unpopular in Massachusetts. There's virtually nothing to be gained there, if they chose to go after a popular Republican."