School leaders in Prince George’s County proposed the creation of a new school police force Thursday, saying that the mass shooting at Sandy Hook Elementary School in Connecticut “changed school security the way 9/11 changed travel.”

The call for more police in Prince George’s schools comes as several leaders in Montgomery County push to double the size of the county’s small band of “school resource officers” and as officials in Prince William County consider significantly increasing the number of police officers in county schools.

Just two months after the Dec. 14 massacre in Newtown, Conn., left 20 children and six school staff members dead, the theoretical discussion about how best to secure the nation’s schools is making its way into reality. As schools work to tighten security measures, proposals for more police on campuses are now part of budget discussions across the region and across the country.

Police have become a central focus in many areas. President Obama has proposed $150 million in funding for school-based officers, psychologists, social workers or counselors. In Virginia, the governor’s school safety task force last week urged restoring state funding for such officers, which had been cut in recent years. The next day, Gov. Robert F. McDonnell (R) urged the legislature to make restoring and enhancing that funding among its highest priorities.

Nationally,a Washington Post-ABC poll in January showed that 55 percent of the public would support placing armed police or trained security guards in the nation’s schools.

“People want to do something, and this seems to be the most direct way to improve school security,” said Corey A. Stewart (R-At Large), chairman of the Prince William Board of County Supervisors, who is pushing to expand police coverage by 15 positions at a cost of about $1.5 million in the first year and $1.3 million in later years.

For Stewart, the proposal is a turnaround: Last fall, he wanted to cut four school-based police positions to save more than $500,000. He said Sandy Hook shifted his thinking. “It’s not going to be cheap,” Stewart said, “but I think it’s going to be worthwhile.”

In Prince George’s, Michael E. Blow, the school system security director, recommended Thursday that the Board of Education spend about $8 million to enhance security at county schools in light of the Connecticut shootings. The proposal, made on behalf of Interim Superintendent Alvin Crawley, includes installing electronic-controlled access and panic buttons in the front offices of each school, installing cameras at 65 schools and creating the new police force.

The police force, which could serve warrants and make arrests, would cost $2 million and be similar to the force that patrols Baltimore city schools, said Briant Coleman, a spokesman for the school system.

“The gauntlet was dropped when that individual took the actions he took at Sandy Hook,” Blow said.

Still, budget constraints are widespread, and some argue that schools need more guidance counselors, not police. The National PTA, while lauding the larger Obama plan, voiced disappointment in the police expansion, saying schools should be completely gun-free. Civil rights groups warn that more police in schools will mean more arrests and citations, often for behavior that once meant a trip to the principal’s office.

There is also confusion about what school resource officers really do in many places. Their jobs are not focused on standing guard at the door. Their focus is mostly students.

A snapshot of how many armed police, called school resource officers, are posted in the region’s schools.

The officers are a police presence — armed, in uniform, in hallways and cafeterias and at after-school events. But the ideal, police officials said, is to forge relationships with students, teach the law and intervene when possible — to prevent a fight, for example, or intercept a weapon before someone gets hurt.

They also make arrests, investigate tips, pick up truant teenagers, and appear in court.

“It’s a more complex role than standing at the front door with a gun on your hip,” said Fred Ellis, director of safety and security for Fairfax County schools.

A survey of the Washington area shows school resource officers work in nearly all high schools in the region.

The exception is Montgomery, which has six resource officers for 25 high schools. Security is provided mostly by more than 200 unarmed security staff members, with support from municipal and county police officers.

With budget hearings coming in the spring, proponents are pushing to double, up to 12, the number of designated school resource officers next year. Political support is greater after Sandy Hook, they say. County Executive Isiah Leggett (D) also is “looking for opportunities to expand, if resources permit,” a spokesman said.

Sandy Hook spurred a quick calculation of the cost for adding police to all 139 elementary schools in Fairfax: about $20 million a year. Fairfax — as well as Loudoun County and Alexandria — already has officers in all middle schools and high schools.

Few in Fairfax have urged a high-cost expansion. “Are we going to put police in all of our elementary schools, as opposed to investing in other things, like early childhood education?” asked School Board member Ted Velkoff (At Large).

At a public meeting in Arlington County last week, parents had numerous questions about police in schools. They asked about staffing, what typical days are like, and whether officers are capable of fending off an attack like the one in Newtown. Arlington, with 36 campuses, has 10 school resource officers.

Cpl. Kyle Anderson, the school resource officer at Arlington’s Wakefield High School, said he hoped his police training would help if extreme violence broke out. Now his days are often focused on getting to know students and their problems, which include bullying and theft.

Fights, thefts and electronic violations — threats or sexting — are especially common problems for school resource officers, said Sgt. Bill Fulton, who supervises officers in western Fairfax. He said officials make efforts to find officers with the right personality for the job. “Kids get comfortable with you, and they tell you things,” he said.

Nationally, school systems have cut back on school resource officers in recent years as budget pressures have mounted, said Mo Canady, executive director of the National Association of School Resource Officers, which estimates that more than 10,000 such officers were stationed in the nation’s schools before the Newtown shootings. Numbers appear to be up in recent weeks, he said.

On the first day of school in August, a 15-year-old student allegedly opened fire in the cafeteria of Perry Hall High School in Baltimore County. Police said the student brought his father’s shotgun to school — with 21 rounds of ammunition and a bottle of vodka — and attacked randomly, hitting a 17-year-old before a guidance counselor subdued him.

People on both sides of the debate find support for their views in such incidents.

Perry Hall had two school resource officers: One was in the cafeteria, police said, and the second was taking a day off.

Critics of putting more police in schools point out that the counselor, not the police officer, stopped the shooting. They also say that, day to day, police often become involved in minor infractions and that federal data show that minority students are more likely to be arrested than white students.

“Anyplace that increases police presence should expect they will see a spike in arrests of those young people that the officers are there to protect — and not for things that create a danger to the school,” said Judith Browne Dianis, co-director of the Advancement Project, a civil rights organization.

Maryland Del. John W.E. Cluster Jr. (R-Baltimore County), whose district includes Perry Hall, said that the police presence helped on the day of the shooting, allowing an officer to take the suspect into custody immediately.

Cluster views police presence as important at all schools, and after the Connecticut shooting, he proposed a Maryland bill to station an officer in any school that doesn’t have one and pay for new hires with state gambling revenue earmarked for education.

Maryland officials estimate that 21 percent of school sites have at least a part-time school resource officer. In Virginia, 47 percent of the schools have at least a part-time police presence, according to recent data.

In Montgomery, supporters of the school resource officer program have redoubled efforts. School board member Michael A. Durso, who worked as a principal for 32 years, said he knows the difference between high schools with officers and those without.

“I can tell you it’s two different worlds,” Durso said, recalling that in 2009, while he was principal at Springbrook High School, a potential attack was intercepted by a school resource officer. “There are no statistics on things that don’t happen. When you prevent incidents, there’s no tally sheet.”

Fredrick Kunkle contributed to this report.