Story highlights Moderate Republicans up for re-election may face pressure to embrace some type of ban on gun purchases for people on the no-fly list

Sen. Kelly Ayotte of New Hampshire indicated she may support such a measure

Washington (CNN) Republican presidential contenders and House leaders have loudly opposed the idea of banning people who are on the U.S. no-fly list from purchasing firearms.

But for Senate Republicans who face competitive re-election battles in 2016, it could be a different story.

The concerns the GOP has broadly expressed about due process aren't gone, but at least one incumbent senator is offering an affirmative position, saying she favors such a ban, even as she insists on more safeguards than Democrats have proposed.

Sen. Kelly Ayotte, a Republican from the key early-voting presidential state of New Hampshire, was a bellwether, tweeting Sunday night: "We need to come together now &pass law 2 stop those on no fly list from buying guns, w/ due process for Americans who are wrongfully on list"

We need to come together now &pass law 2 stop those on no fly list from buying guns, w/ due process for Americans who are wrongfully on list — Kelly Ayotte (@KellyAyotte) December 7, 2015

Her language -- embracing a ban rather than immediately rejecting it -- reflects the different realities of the 2016 election cycle for Republicans.