WASHINGTON — More than seven in 10 residents of Kentucky want their new governor, Matt Bevin, to keep the state’s expanded Medicaid program as it is, according to a new poll from the Kaiser Family Foundation. And more than half of respondents described Medicaid as important for themselves and their families, underscoring the program’s substantial reach in the state and the challenges Mr. Bevin may face if he seeks to scale back or modify it.

Mr. Bevin, a Republican who took office Tuesday, is an opponent of the Affordable Care Act who earlier this year called for reversing the Medicaid expansion on the grounds that it was unaffordable for the state. He has since backpedaled to say he will seek changes requiring Medicaid enrollees to have “skin in the game,” such as by charging them monthly premiums.

“I do not intend to re-enroll people at this same level going forward,” Mr. Bevin said in a news conference after his election.