In Kansas, Gov. Sam Brownback, among the most conservative, is calling for full-day kindergarten for all students. In her State of the State address, Gov. Susana Martinez of New Mexico, a Republican, talked about increasing teacher salaries…

Still, Ms. Martinez’s view was not shared by her fellow Republicans in Missouri, where Republican legislators sharply criticized Governor Nixon’s proposal to increase education spending by $493 million. “It is really unfortunate that this governor’s only solution is to throw money at problems,” said Tim Jones, the speaker of the Missouri House.

In some states where one party controls both the governor’s seat and the legislature, intraparty battles are looming over how to use the surpluses.

One example is in California, where Gov. Jerry Brown, a Democrat, called in his State of the State address for more money to go into a rainy-day fund rather than into renewed spending — over the loud objections of some Democratic legislators who want to restore more of what had been trimmed in recent years.