After voting to turn off sequestration’s across-the-board cuts to the military last week, House Republicans will look to reinforce their defense bona fides this week on the floor and in the Appropriations Committee.

The House will take up the fiscal 2013 National Defense Authorization Act starting Wednesday, which would authorize about $643 billion for national security programs, topping President Barack Obama’s request by nearly $4 billion.

At the same time, the Appropriations Committee will take up four subcommittee bills dealing with national security spending, including the defense bill, which also has more funding than the president requested.

Two appropriations bills will be in committee Wednesday and another two on Thursday, barring any unexpected amendments that could hold up the process.

Some of those bills could reach the floor as soon as the end of May, after the House returns from a weeklong recess that begins May 21.

It is still up in the air whether House leaders will, over the objections of some Republicans, bundle those bills, which deal with funding Defense, Homeland Security, State and foreign operations, and military construction and Veterans Affairs. The committee-passed Energy and water development bill, which contains funding for the nation’s nuclear arsenal, could be part of the package as well.

On the messaging front this week, Republican leaders remain intent on avoiding the pitfalls of social issues and sticking to an economic message, senior aides said. “We’re talking about jobs and they’re not,” one leadership aide said.

Speaker John Boehner (R-Ohio) and House Budget Chairman Paul Ryan (R-Wis.) will deliver remarks at the Peter G. Peterson Foundation Fiscal Summit on Tuesday, driving home their vision for the economy.

Indeed, even on issues that are not, strictly speaking, economic in nature, Republicans will look to use them to demonstrate the differences on fiscal matters between Republicans and Democrats.

For instance, when the House takes up the Violence Against Women Act this week, rather than focus on the social aspects of the legislation, the GOP will use the bill to launch an economic-based counterattack against Democrats’ message that Republicans are waging a “war on women.”

“Republicans are combating the war-on-women narrative by talking about how the Obama economy has adversely affected women,” a GOP aide explained.

Democrats, however, will argue that the House should have taken up the version of the Violence Against Women Act that passed the Senate rather than the House version, which they say rolls back protections against women.

But controversial amendments tacked to the defense authorization bill could also threaten to derail the GOP jobs message, especially as Obama’s stated support for gay marriage might continue to drive headlines.

Rep. Steven Palazzo (R-Miss.) tacked an amendment to the reauthorization that would prohibit same-sex marriage ceremonies on military bases, while Rep. Todd Akin (R-Mo.) added another amendment that would shield chaplains who object to the repeal of “don’t ask, don’t tell” from reprisal.

Obama has “used the military as a campaign prop to advance the liberal agenda,” Akin said in a statement. “Whatever Obama’s views may be, I find it appalling that he would so blatantly use the military for political cover on this controversial issue.”

But just as Boehner sidestepped questions on gay marriage last week, don’t look for leadership to either engage in the gay marriage debate or tolerate having their messaging hijacked by social conservatives during the defense reauthorization bill.

The leadership aide said there has been “no discussion” of gay marriage during top-level discussions on the agenda, and Boehner has made it clear he won’t be pulled into a religious war if he can help it.

“The president and Democrats can talk about this all they want, but the American people are focused on jobs and the economy,” the Speaker told reporters Thursday.

“I’m going to stay focused on jobs,” he added.

House Democrats, meanwhile, hope to continue to strike out at their counterparts over the House-passed budget and last week’s reconciliation package, which included cuts to social programs for the poor.

House Budget ranking member Chris Van Hollen (D-Md.) and House Democratic Caucus Vice Chairman Xavier Becerra (Calif.) will also be at the Peterson fiscal summit, offering an economic vision to compete with Boehner and Ryan’s. “It’s Republicans protecting millionaires over the middle class,” one aide said.

The House might also hand embattled Rep. Michael Grimm (R-N.Y.), a former FBI officer, a political win during National Police Week if it proceeds to vote on his bill to institute a national “Blue Alert” to help find people suspected of killing or injuring law enforcement officers. The system would work much like the Amber Alert, which helps locate abducted children. The bill might come up under suspension of the rules.