Mr. Haslam said in an interview that the law had passed by a wide margin, so the Legislature could have easily overridden a veto. And he said that while he feared that the law would muddy state policy for teachers rather than clarify it, he had been assured by state education officials that it would not actually change the way science is taught in Tennessee.

But he said he also worried that the law could damage the reputation of a state that was home to another famous legal battle over the teaching of evolution, the Scopes “monkey trial” of 1925.

“One of the things as governor, you’re always out — I’m out selling Tennessee all the time to businesses and other folks,” Mr. Haslam said during a recent visit to New York, adding that the state had heavily focused on the teaching of science, technology, engineering and mathematics in recent years. “So you worry about misperceptions, sure. I wouldn’t be honest if I said I didn’t do that. But if I thought it was actually going to harm the scientific standards, I would have vetoed it.”

When Gov. Bob McDonnell of Virginia, the chairman of the Republican Governors Association, appeared on the MSNBC program “Morning Joe” last week to talk about his state’s successful efforts to lower its unemployment rate, he found himself facing a number of questions about something else: the law he signed requiring women to undergo an ultrasound before getting an abortion, which received a great deal of attention this year.

“We had 860 bills this session; one of them reached my desk on abortion,” Mr. McDonnell said. “So to say that it was some broader trend is not the case.”

So far this year, 75 bills placing restrictions on abortion have passed at least one legislative chamber, which is more than normally pass in an election year, according to a tally by the Guttmacher Institute, a research organization. But it is below the pace established last year, when Republicans first won control of many statehouses and a record 127 restrictions were passed by at least one house of the legislatures during the first quarter.

Bills expanding gun rights have passed in a number of states. Maine recently joined several others that passed a bill prohibiting restrictions on the right to carry or sell firearms during a declared state of emergency. Arizona enacted a law requiring law enforcement agencies to sell forfeited guns within a year, rather than destroying them, as many local agencies do. Oklahoma enacted a law that will limit the liability that gun ranges face for accidents.