Bonner's comments confirm what House GOP leaders have said for several weeks now — that the House might consider a Senate-passed gun bill, but won't develop its own bill. House Speaker John BoehnerJohn BoehnerTrump, GOP fumble chance to govern ObamaCare gets new lease on life Ryan picks party over country by pushing healthcare bill MORE (R-Ohio) has said the House would "review" any bill the Senate can pass.

But with the Senate's failure to pass a bill earlier in the month, the House position makes it increasingly unlikely that Congress will pass anything related to guns.

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The shooting in Newtown, Conn., has prompted gun control advocates to seek new federal rules, including an assault weapons ban and a ban on high-capacity ammunition clips. However, Senate Majority Leader Harry ReidHarry ReidThis obscure Senate rule could let VP Mike Pence fully repeal ObamaCare once and for all Sharron Angle to challenge GOP rep in Nevada Fox's Watters asks Trump whom he would fire: Baldwin, Schumer or Zucker MORE (D-Nev.) only allowed a bill to come to the floor that did not include those items.

And while he allowed votes on those amendments, each required a 60-vote threshold to pass, making them impossible to pass given GOP opposition. A bipartisan proposal on background checks also needed 60 votes and failed to pass.

In his remarks in Alabama, Bonner added another wrinkle to the gun debate by saying that if a gun bill were considered, he would want language in it aimed at curbing violence in movies and video games. He said mental health issues should also be addressed.

Violence in entertainment and mental health have been pushed by other Republicans, many of whom argue that these issues are partly responsible for gun violence. They also argue that simply making it harder for law-abiding people to buy guns will not curb violence.

"Until we talk about the comprehensive issues with entertainment, the video games or mental health, I don't think, even if you banned all of the guns or high-capacity magazines or the … automatic weapons, I don't think you could stop [the gun violence]," Bonner said.