ST. PAUL — Frustration is festering at the Capitol, where Minnesota’s divided government has largely meant lawmakers from both parties being thwarted from the policies they’d love to enact.

Minnesota is the only state where different parties control the House and Senate. Democratic Gov. Tim Walz, Democratic House Speaker Melissa Hortman and Republican Senate Majority Leader Paul Gazelka have kept in close touch as they try to make it work. Walz has already signed some bipartisan legislation. More should reach his desk soon. But many proposals with a sharper partisan divide have stalled out.

A group of Democrats calling themselves the “Senate Committee on Banned Bills” will hold an unofficial hearing Monday on bills the Republican majority has refused so far to hear.

That includes requiring universal criminal background checks on gun transfers; preserving an expiring tax on health care providers that helps fund health care programs; encouraging the hiring of more teachers of color; creating a paid family and medical leave system; restoring the rights of felons to vote when they get out of prison; and enacting a state Equal Rights Amendment.

“These bills have huge public support and are common sense ideas,” Sen. Matt Little, the “chair” of the group, said in a statement. “But the Senate can’t make good decisions if major options aren’t even on the table. Partisan games like this are rigging our democracy, and blocking bills that voters really want.”

Gazelka recently gave a little ground, saying Senate Republicans might consider hearings on gun control bills if they pass the House first. Besides the background checks, the other Democratic gun priority is a “red flag” bill that would allow relatives or police to ask a judge for an “extreme risk protection order” that would allow temporary confiscation of guns from people deemed an imminent risk to themselves or others.

But Gazelka also said Republicans would then bring up GOP proposals for a “stand your ground” law expanding when a gun owner can shoot in self-defense, and to raise penalties for illegal gun transfers.

Senate Democrats had hopes earlier that they might be able to peel away a few moderate suburban Republican senators to force wins on gun control and some other issues, but that hasn’t happened yet. The Senate GOP has a three-vote majority, 35-32. House Democrats hold a 16-vote, 75-59 majority. Big or small, majorities decide which bills get heard and which ones don’t.

There’s similar frustration among House Republicans, where Deputy Minority Leader Anne Neu said they’re steamed about three issues where their bills haven’t gotten much traction.

Neu said they got a hearing in one committee on a bill to extend the state’s health care reinsurance program, but Democrats favor a different approach for keeping premiums down, so it remains stuck in a different committee. On Thursday, Democrats blocked a bill that passed the Senate earlier in the day to prohibit the Commerce Department from further appeals against Enbridge Energy’s plan to replace its Line 3 crude oil pipeline. And she said they’ve gotten nowhere so far with bills to fight fraud in the Child Care Assistance Program.

“Let’s be honest,” she said. “There are tons of bills that we would love to have heard that are just not going anywhere.”

Gazelka often says Minnesotans have shown they like divided government because they keep voting for it.

“There are pros and cons to it,” Neu said. “It forces us to have good, thorough conversations about things. That’s really important. … The problem is when we have one party stonewalling the other.”