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"
Her language -- embracing a ban rather than immediately rejecting it -- reflects the different realities of the 2016 election cycle for Republicans.
Those on the presidential debate stage are still courting the party's most conservative elements, where pro-gun groups such as the National Rifle Association are powerful.
But the party's vulnerable senators largely represent blue or purple states, which means they've already shifted their focus to the middle of the electorate.
Another Republican whose seat is endangered, Sen. Mark Kirk of Illinois, last week broke GOP ranks and voted for a measure that would have banned people on the U.S. terror watch list from buying guns. That list is a broader group than the no-fly list.
At the time, Republicans offered an alternative measure that would have allowed federal authorities 72 hours to offer probable cause that a gun purchase should be blocked, but like the ban on terror watch list members purchasing firearms, it failed in the Senate last week.
President Barack Obama put more pressure on Congress in a Sunday night address
to the nation from the Oval Office, calling on lawmakers to ban no-fly list members from buying guns.
"What could possibly be the argument for allowing a terror suspect to buy a semi-automatic weapon?" Obama said.
As a result, Republicans such as Ohio Sen. Rob Portman, Wisconsin Sen. Ron Johnson and Pennsylvania Sen. Pat Toomey could face more questions about whether they'd support that narrower ban.
Their offices deflected or didn't answer questions about their positions on such a ban Monday.
Instead, most pointed to last week's vote, with Toomey saying in a statement that the Democratic-backed measure banning gun purchases for all terror watch list members "provided no meaningful opportunity for innocent U.S. citizens to challenge being erroneously placed on a terrorist list, and that is why I opposed it."
Regardless, Republican leaders on Capitol Hill haven't indicated an interest in taking up such a measure before they leave town this month.
House Speaker Paul Ryan
, in an interview Monday with the Wisconsin State Journal, called the President's call for action on legislation addressing the no fly list "a distraction."
"A mid-level bureaucrat can put anybody on a no-fly list with no due process rights," Ryan said.