The White House on Monday signaled that President Donald Trump is willing to back at least one bipartisan measure to strengthen the national instant check system for those who buy firearms, as Democrats in the House and Senate continued to argue that action by the Congress on gun violence is long overdue.

"While discussions are ongoing and revisions are being considered, the President is supportive of efforts to improve the Federal background check system," said White House Press Secretary Sarah Huckabee Sanders.

In a written statement sent to reporters, Sanders said the President spoke to Sen. John Cornyn (R-TX) on Friday; the Texas Republican has a bipartisan bill with Sen. Chris Murphy (D-CT), which would force states and federal agencies to submit more information into the instant gun check system.

After a mass shooting last November in Sutherland Springs, Texas, where 25 people died, the Air Force acknowledged that the killer - who received a 'bad conduct' discharge from the military - should not have been able to buy guns, but those records were never placed in the instant check system.

"For years agencies and states haven't complied with the law, failing to upload these critical records without consequence," Cornyn said in November when he introduced this bipartisan gun measure."

Democrats had hoped there would be action on that measure - just like they had hoped there would have been action to ban "bump stocks" after the mass shooting in Las Vegas, action on the "No Fly, No Buy" measure after the Orlando Pulse Nightclub shooting, and then the "FixNics" bill after the Texas shooting.

"Kids shouldn’t have to live in fear of being shot at school," said Rep. Seth Moulton (D-MA).

Last week's shooting in Florida simply put all of those requests for legislation to deal with guns on repeat for Democrats.

"We can't ignore the issues of gun control that this tragedy raises," said Sen. Kamala Harris (D-CA). "And so, I'm asking - no, demanding - we take action now.”

Democrats would certainly like to do much more than the 'FixNics' bill, or banning bump stocks, as other ideas have popped up in recent days, like not allowing anyone under age 21 to buy weapons like an AR-15.

But as the President returned to Washington on Monday evening from a long weekend at his Florida retreat, it wasn't clear if his support for one bipartisan plan would actually mean action - as GOP leaders have not put such measures on the fast track to a vote in the House and Senate.

On Sunday, when the President met with House Speaker Paul Ryan in Florida, the two men discussed a series of issues, including "the recent tragedy in Parkland, Florida."

The White House statement on their meeting did not characterize whether legislative action was discussed.

No action will happen on anything gun-related this week - as the Congress won't be back on Capitol Hill for votes until February 26.