Already, New York Gov. Andrew Cuomo and Mr. O’Malley are engaged in a game of one-upmanship, with Mr. Cuomo moving to approve gay marriages and enact the nation’s toughest gun ban and Mr. O’Malley following suit. But Mr. O’Malley took matters a step further in pushing to end Maryland’s death penalty — a move Mr. Cuomo couldn’t match, since that state’s court system had effectively ended executions years ago.

“For all the years where people pointed to Republicans and said, ‘They had an abortion litmus test and won’t elect anyone who is not pro-life,’ the reality is the Democratic Party now has a series of new litmus tests in regard to new candidates, and these governors want to make sure they have those boxes checked,” said Todd Eberly, coordinator of public policy studies at St. Mary’s College of Maryland.

“Public opinion trends on these issues may have emboldened liberal governors to push certain issues more strongly in the current climate,” said Mark J. Rozell, a political-science professor at George Mason University. “In so doing they can burnish their credentials nationally with the liberal wing of the party, which of course is so hugely influential in the presidential nominating process.”