SANTA FE, N.M. — A plan to slash New Mexico state agency spending by nearly 3 percent with the exception of public safety and child welfare programs was approved Wednesday by the state House of Representatives.

The proposal closely resembles a Senate-approved bill, and House Republican majority leader Nate Gentry said he had negotiated a “handshake” compromise with Senate leaders that resolved disagreements by cutting higher education funding by 5 percent. House Republicans initially advocated for greater cuts to public colleges, universities and vocational schools.

The House bill would deepen Senate approved cuts to 5.5 percent of current operating budgets at most agencies, including departments overseeing public health programs, taxation and revenue, economic development, state museums and historic sites, along with the state attorney general’s office.

The 36-32 vote in the House advances a key budget solvency provision as lawmakers confront a nearly $600 million general fund shortfall linked to a downturn in oil and gas markets.

“This is about the least fun I’ve ever had in Santa Fe is figuring out what areas of government to cut,” Gentry said. “Gridlock cannot prevail here because if it does, government shuts down.”

House deliberations extended late in to the evening, after an hours-long recess in which House Democrats and Republicans met separately behind closed doors.

House minority leader Brian Egolf voted against the House amendments to the original Senate bill, saying more consideration needed to be given to revenue increases.

“Because of the views of a few,” he said, “we’re not really allowed to talk about tax reform in a meaningful way.”

Republican House lawmakers cited concerns about violent crime and child abuse as they sought to maintain funding for State Police and child protective services.

Republican Gov. Susana Martinez and legislative allies also are pushing to revive capital punishment in response to the recent killings of two police officers and the sexual assault, killing and dismemberment of a 10-year-old Albuquerque girl. New Mexico repealed the death penalty in 2009 under Democratic Gov. Bill Richardson.

Egolf said it made little sense to cut funding to the attorney general’s office if lawmakers are concerned about crime.

“I don’t understand why they are recommending a 5.5 percent cut as the state’s top law enforcement agency,” Egolf said. “Why not hold them harmless?”

The Democrat-led Senate has approved a slate of budget solvency measures that also would sweep money from idle government accounts and close tax loopholes. House Republicans have resisted Senate proposals to suspend corporate income tax decreases, collect taxes on internet sales by out-of-state companies like Amazon or transfer cash balances from local school districts to the state general fund.

“This has gone past belt-tightening and entered the amputation stage,” said Rep. Bill McCamley, D-Las Cruces. “These cuts will have a real lasting effect on the people of this state.”

Republican lawmakers said delaying the tax decrease could discourage business investments and aggravate the economic difficulties. Martinez steadfastly opposes any tax increases.

House-approved cuts to higher education and per-student funding at public schools would come with the added recommendation that administrative areas outside the classroom be targeted.

Republican Rep. Dennis Roch of Logan, sponsor of the appropriations amendments, said agency heads would have broad discretion to shift money among programs and set priorities. Democrats warned that funding cuts to higher education might be passed on to students in the form of higher tuition or fees.

Roch’s proposal would reduce funding to the judiciary by 3 percent. Rep. Antonio Maestas, D-Albuquerque, said those reductions threaten to bog down criminal prosecutions and undermine efforts by Republicans to address violent crime.

The House is poised to vote this week on a bill to reinstate the death penalty for convicted killers of police, children and corrections officers.