TALLAHASSEE, Fla.  Rick Scott, the conservative Republican billionaire who plucked the governor’s job from the party establishment in November with $73 million of his own money and the backing of the Tea Party, vowed during his campaign to run the troubled state like a corporate chief executive (which he was) and not a politician (which he proudly says he is not).

And now it has become a problem, some of his fellow Republicans say.

“The governor doesn’t understand there is a State Constitution and that we have three branches of government,” said State Senator Mike Fasano, a Republican from New Port Richey who upset Mr. Scott with rough handling of his staff during a testy committee hearing. “They are talking about the attitude that he is still the C.E.O. of his former health care corporation, and that is not going to work in this state, in Tallahassee, in my district. The people believe in three branches of government.”

Republican lawmakers in Florida were hoping for a smoother transition. Instead, they say, they got top-down management from a political novice.

With the Legislature convening on Tuesday for a potentially arduous two-month session that is bound to usher in major cuts in spending and jobs and radical changes to education, pensions, unemployment benefits and Medicaid, the governor will be tested on a broader, more public scale. Florida faces an estimated $3.6 billion budget shortfall this year and has a stubborn 12 percent unemployment rate.