State House members struggled to find the votes for tighter gun control Monday as a deadline ticked closer, but they easily passed a series of changes to the mental-health system.

The two issues have been linked by some who say together they will make Washingtonians safer from violent crime. House Judiciary Committee Chairman Jamie Pedersen hoped for steps on both fronts before Wednesday’s deadline to advance legislation.

Taken as a whole, the Seattle Democrat said, the bills should help reduce violence “in the ways that we can.”

Also on his list, and approved unanimously Monday by the House: a new kind of court order to protect stalking victims. It’s motivated by the 2010 Tacoma shooting death of Birney Elementary School teacher Jennifer Paulson by a man who was under an anti-harassment order to stay away.

The mental-health proposals appear to have broad support in the Senate, where they go next, and Gov. Jay Inslee gave a thumbs-up Monday to the House’s general direction on the issue. But ultimately, their fate will hinge on the budget process.

A lack of funding is what has allowed bottlenecks that keep patients waiting in hospitals and jails. It also keeps policies alive that make it harder to keep potentially dangerous patients detained.

The state faces a roughly $1 billion two-year shortfall and an obligation to schools that could reach as much as $1.4 billion. But House Majority Leader Pat Sullivan has said lawmakers also have an obligation to enhance funding for mental health.

The combined cost of what the House approved for mental health Monday would be roughly $23 million over the two-year period, according to the most recent estimates.

At least one measure will probably require more beds at state psychiatric hospitals. It would make it easier to keep people detained who have been found incompetent to stand trial for violent felonies – people like Tacoma’s Jonathan Meline. He was released from Western State Hospital last year and killed his father, Rob Meline, while he lay in his bed in his Tacoma home.

“I think there will be some concerns on this side of the aisle (among Republicans) with the cost implications of the bill,” said a supporter of the measure, GOP Rep. Jay Rodne of North Bend.

The Senate unanimously passed similar legislation last week. In the House Monday, a bill passed 87-to-11 after lawmakers changed it to pick up support from some Democrats, including Lakewood Rep. Tami Green, by allowing alternatives to hospital confinement. Green described the alternatives as a sort of mental-health probation.

Another costly piece is the delayed implementation of less-strict standards for detaining potentially dangerous patients. The rules would allow more consideration of patients’ past behavior in addition to the immediate threat they pose.

Passed in 2010, the changes were delayed until mid-2015 but the House voted unanimously Monday to move them up to mid-2014. It would require speeding up a state effort to build more space for mental-health evaluations and more kinds of outpatient treatment.

The Senate passed a similar bill a few hours later, also unanimously.

Another proposal the House approved 95-to-3 Monday would create a task force to look at the whole mental health system and move toward opening step-down facilities that the Legislature authorized in 2005 but didn’t fund. A similar proposal also passed the Senate unanimously last week.

DSHS officials say moving patients out of state hospitals would help unclog backups that have left patients stranded in local hospitals for days.

Another backlog is in local jails, where it’s common for mentally ill criminal suspects to wait for weeks to be evaluated. By a 92-6 vote, the House Monday passed a change requested by Pierce County officials that would let them farm out some evaluations to the private sector.

Green struck a hopeful tone in supporting the measures.

“Mental illness is a medical condition, not a character flaw,” said Green, and she added later: “The great thing about it is that people can recover, and they can get better, and they can have happy, fulfilling lives where they can even have jobs and become taxpayers again.”