SANTA FE, N.M. — A three-strikes criminal sentencing proposal won approval in the New Mexico House of Representatives on Sunday, amid ongoing deliberations over how to close a major budget shortfall during a special legislative session.

The sentencing bill would expand the list of violent crimes that mandate life behind bars for a third conviction. It was unclear when or if the Senate would take up the proposal, one of three criminal justice initiatives backed by Republican Gov. Susana Martinez. The Senate has adjourned after approving a slate of deficit reduction measures to await a response from the House, where committees spent the weekend in budget discussions.

The House-approved three-strikes bill would add a list of 16 additional crimes to the existing mandatory sentencing law for repeat violent offenders. A nearly identical bill approved by the House earlier this year was never voted on by the Senate.

Senate Democrats including majority floor leader Michael Sanchez say they are focused foremost on the state’s fiscal crisis and that criminal justice reforms can wait.

The chief sponsor of the three-strikes law, Rep. Paul Pacheco, described the original 1994 three strikes law as “a joke” that has never been applied because it covers only five criminal offenses.

“The current law as it stands, in my humble opinion, is ineffectual,” said the Albuquerque Republican and former law enforcement officer.

Rep. Sheryl Williams Stapleton, D-Albuquerque, condemned efforts to approve tougher sentencing at the same time that the Legislature is considering budget cuts to state courts, prosecutors, public defense attorneys and social services programs.

“You cut the hand of the one that takes care of you,” she said. “We should provide the resources before it gets to the three strike law.”

Pacheco called the sentencing proposal just one “piece of a very complicated puzzle” for reducing violent crime. “It’s not a silver bullet,” he said.

The New Mexico Sentencing Commission estimates the three-strikes expansion could cost to state government as much as $60 million over 15 years in increased incarceration costs.

Martinez and allied lawmakers say proposals for stricter sentencing — including the reinstatement of the death penalty — respond to a groundswell of public concern about violent crime, partly in responses to the recent shooting deaths of two police officers and the sexual assault, killing and dismemberment of 10-year-old Victoria Martens in Albuquerque in August.

In committee meetings Sunday, House Republican outlined new budget solvency proposals that would preserve current spending at the Departments of Public Safety and Children, Youth and Family while implementing steeper cuts at a host of other state agencies.

The Senate has approved agency funding cuts totaling $175 million, while a House appropriations committee discussed possible amendments Sunday that would make steeper cuts to higher education budgets, including a possible 8 percent budget decrease at the University of New Mexico. Consideration of those and other amendments — one restricting reductions in public school funding to administrative expenses — were postponed until the full House considers the legislation.

The appropriations committee on Sunday recommended full House approval of a Senate proposal to shore up the state general fund with money once earmarked for stalled local construction projects.

A House taxation committee abandoned a proposal to speed up reductions in so-called hold harmless payments to local governments, funding originally designed to blunt impact of halting taxes of gross receipts taxes on food and medicine.

A Senate-proposal to delay corporate income tax reductions for two years stalled in a House committee on taxation Saturday, over the objections of several House Democrats.

New Mexico finished the budget year in June with a $131 million deficit after exhausting operating reserves, and has a projected budget shortfall for the current year of $458 million if budget changes are not made. The state’s credit rating is under review by a major credit rating agency for a possible downgrade that would increase borrowing costs.

The Legislature has approved one deficit reduction measure that would decrease contributions to a health care fund for retired state employees and halt scheduled increases in funding to a state fire protection fund.