SANTA FE, N.M. — On the opening day of a special legislative session, efforts to institute tougher criminal sentences and bring back the death penalty to New Mexico took center stage in the Republican-controlled House of Representatives, while the Democrat-led Senate unveiled detailed plans for closing a major budget shortfall.

Legislators prepared Friday to work through the weekend to resolve budget deficits tied to a sustained downturn in energy prices, as allies of Republican Gov. Susana Martinez pushed forward with a trio of criminal justice bills.

Martinez is seeking to reinstate the death penalty in response to the killings of two police officers in separate shootings in August and September by wanted fugitives. The proposed legislation also responds to last month’s horrific sexual assault, killing and dismemberment of 10-year-old Victoria Martens in Albuquerque.

“I am here today as her voice for justice,” said Rep. Monica Youngblood, R-Albuquerque, a sponsor of the death penalty proposal.

Dozens of people lined up to make public comments about the bill and capital punishment issues at the committee hearing — including several relatives of murder victims, police, religious leaders, defense attorneys, prosecutors and several high-ranking public safety officials appointed by the governor.

Opponents of the legislation repeatedly objected to the relatively short timeframe of consideration during a special session that may last just a few days. They said they had little time to review the language of a bill that was published Friday afternoon, hours before the first committee deliberations.

Rep. Sheryl Williams Stapleton, D-Albuquerque, raised a series of objections to the bill, repeatedly pressing sponsors for evidence that it would deter crime. Rep. Gail Chasey, D-Albuquerque, said law enforcement authorities should be surveyed widely to see if the money needed to reinstate the death penalty would be better spent in other areas to protect police and reduce crime.

The bill’s second sponsor, Rep. Andy Nunez, R-Hatch, voted in favor of repealing New Mexico’s death penalty in 2009. But he now supports reinstatement after the shooting death in August of Hatch police Officer Jose Chavez. He listed the names of six police officers killed in the line of duty in New Mexico since the repeal of the death penalty as good reason for reinstating capital punishment.

Terri Cole, president of the Greater Albuquerque Chamber of Commerce, said the bill “specifically responds to the problems that are out of control, and that is that our police, who are trying to protect, us are being targeted.”

The House also heard tearful testimony from relatives of victims of violent crime as it took up a proposal to expand “Baby Brianna’s Law” to require mandatory life sentences for people convicted of intentional child abuse resulting in death, regardless of a child’s age. The House judiciary committee endorsed the bill 12-1.

Rep. Conrad James, R-Albuquerque, urged lawmakers to take a more pro-active stance to ensure appropriate punishments are in place to respond to deadly child abuse. “This is not about preventing child abuse, this is about making sure that the proper penalties are in place before these actions take place,” James said.

Democratic lawmakers accused the House Republican majority of seizing on the anti-crime initiatives to distract public attention away efforts to resolving a major budget shortfall and seek a political advantage in November elections, when the entire Legislature is up for re-election.

“They’re playing politics with people’s grief and sorrow,” said Rep. Brian Egolf Jr., D-Santa Fe, the House minority leader, who himself broke down in tears while debating crime legislation.

Lawmakers also are considering a proposal to expand New Mexico’s three-strikes law requiring a life sentence for criminals with three or more violent felony convictions to include a longer list of applicable offenses. The legislation failed to clear the Democrat-led Senate earlier this year.

New Mexico finished the budget year in June with a $131 million deficit after exhausting operating reserves, as a sustained downturn in energy markets cut into state revenues and rippled through the economy. At last count, the $6.2 billion general fund spending plan for the current year exceeds estimated revenues by $458 million.

The Senate Finance Committee recommended approval for a series of budget-mending bills, including a bill that would suspend the state’s gradual reductions of its corporate income tax. Another Senate proposal would remove the state’s limit on the number of marijuana plants that a licensed producer of medical cannabis can cultivate