Some Republican incumbents in battleground states are looking to compromise on gun control, according to The Hill.

Democrats have pressured Republicans on the issue, but many have not budged regarding gun control legislation. But now they appear to be looking at the issue, although Democrats say it's just an attempt to draw in voters.

Florida Republican Sen. Marco Rubio proposed a bill to prevent terror suspects from obtaining guns and would require that the FBI director and the Joint Terrorism Task Force be contacted when someone under investigation attempts to buy a firearm.

Rubio said he was keeping a promise to Fred and Maria Wright, parents of a victim in the Orlando nightclub shooting in June.

"Today, I'm taking another step toward fulfilling my promise to the Wright family, by introducing legislation that builds on some of the best ideas that have been proposed, and improves them in ways that I hope will make a bipartisan solution more likely," Rubio said.

The Florida senator's bill could achieve its goals lawfully, "without violating the due process and Second Amendment rights of innocent, law-abiding Americans."

Rubio's opponent for Senate reelection, Democratic Rep. Patrick Murphy, called the bill a "sham." Connecticut Democratic Rep. Chris Murphy said Rubio's bill "is just intended to be a footnote in a TV ad," noting that he voted against Republican Sen. Susan Collins' compromise bill on gun control.

Mark Prentice, the spokesman for Americans for Responsible Solutions, a gun-control advocacy group founded by shooting victim and former Rep. Gabby Giffords, said that candidates are beginning to recognize that proposals meant to stop gun violence is "the political high ground."

"You are increasingly seeing candidates running on the issue, and in some cases trying to get right on the issue," Prentice said, adding that his group is working against any "gun lobby-backed plan that masquerades as public policy."

Americans for Responsible Solutions has supported both Democrats and Republicans. In August, Giffords and her husband Mark Kelly endorsed Republicans, Pennsylvania Sen. Pat Toomey and Illinois Sen. Mark Kirk, for their stances on gun control legislation, according to an op-ed on CNN.

The Brady Campaign to Prevent Gun Violence has praised Republican Florida Rep. David Jolly for his legislation to prevent terror suspects from buying firearms. The Hill reports that could boost Jolly in his battle against former Democratic Gov. Charlie Crist.

Observers see progress in the fact that the GOP is mentioning gun control legislation. UCLA law professor Adam Winkler said, "The fact that they're even proposing legislation, and they're promoting it as part of their election campaigns, is novel and does show how much the gun debate is shifting."

The battle between political sides continues over the matter. Democrat Rep. John B. Larson told Roll Call he expected Republicans to ban sit-in demonstrations like the Democrats held in objection to GOP not taking action on gun control legislation.