In interviews, officials said that Gov. Bill Lee, a Republican, was politically constrained by a deeply conservative legislature and a political base that became more uncompromising during the pandemic…

Publicly, he has asked Tennesseans to get vaccinated, but has argued for local control of mitigation measures and against any kind of mandate.

Mr. Lee’s response on Twitter to President Biden’s sweeping vaccine requirement is one example. At the end of a thread of messages, Mr. Lee said: “To be clear: the vaccine is the best tool we have to combat the pandemic but heavy-handed mandates are the wrong approach.”

Some Republican politicians in Tennessee say Mr. Lee’s approach amounts to choosing political expedience over the well-being of the state.