ST. PAUL — Constitutional amendments favored by one political party but not the other, like the two failed measures from 2012 to ban gay marriage and require photo identification for voting, would become much less frequent under a proposal a state Senate committee backed Monday.

Bill sponsors, including Senate Majority Leader Tom Bakk, told the Senate State Government Committee that the state constitution should have a stronger cushion against partisan pressures. Right now, a simple majority vote of the House and Senate sends an amendment to the statewide ballot; the governor has no power to stop it. Bakk’s amendment, if it makes the 2014 ballot and is approved by voters, would require that all proposed amendments clear a 60 percent supermajority in the House and Senate in order to make the ballot.

“I think this is a discussion the Legislature should have this year,” said Bakk, DFL-Cook. “Amending the constitution is really, really important business.”

In 2012, Republicans who controlled the House and Senate sent the voter ID requirement and gay marriage ban to the November ballot over the objection of Democratic Gov. Mark Dayton and DFL legislators, then in the minority. Voters defeated both measures. In 2006, Democrats used the legislative majority to forward an amendment to require that the state’s sales tax on motor vehicles only be spent on transportation projects, which passed.

Sen. Dick Cohen, sponsoring a bill similar to Bakk’s, said none of those amendments would have made the ballot under a supermajority requirement.