Washington (CNN) President Donald Trump cast doubt Monday he could come to an agreement with Democrats on gun control as lawmakers await his proposals to combat deadly shootings.

It was a downbeat signal from Trump on finding common ground with political rivals on the issue, which gained momentum after an August book-ended by gruesome shooting sprees.

Trump discussed gun control for 11 minutes by phone Sunday with House Speaker Nancy Pelosi and Senate Democratic Leader Chuck Schumer. The Democrats promised they would join him for an "historic" Rose Garden signing ceremony if he gets behind a House-passed bill expanding background checks to nearly all gun sales.

But the White House has already threatened to veto that bill, and Trump himself on Monday signaled he has doubts about Democrats' stated motives.

"The big questions are," the President tweeted, "will they 'move the goalposts' and, is this just a ploy to TAKE YOUR GUNS AWAY?"

"I hope NOT on both counts, but I'll be able to figure it out!" Trump wrote.

After more than a month of discussions between White House and congressional officials on guns, there remains little clarity on where Trump stands on expanding background checks. Even in private, Trump has not revealed a final position, according to people familiar with the discussions.

That has led to doubts the President will ultimately put his support behind background checks legislation, including a bipartisan measure from Sens. Joe Manchin, D-West Virginia, and Pat Toomey, R-Pennsylvania, which is more limited in scope than the House bill that passed in February.

Waffling on background checks

After a pair of shootings in Texas and Ohio at the beginning of August, Trump voiced support for expanding background checks. He was urged on, in part, by daughter and senior adviser Ivanka Trump, along with some Republican senators such as Toomey who support such a move.

But others in his inner circle cautioned the move might be politically unpopular among his supporters.

The debate over gun control has galvanized Democrats, who cite polls showing the vast majority of the country is with them in supporting expanding background checks. At a debate last week among Democratic primary contenders, former Texas. Rep. Beto O'Rourke vowed to enact mandatory buybacks on some assault weapons.

"Hell yes, we're going to take your AR-15, your AK-47," he said, a comment Republicans seized upon afterward.

In his tweet on Monday, Trump appeared to echo his fellow Republicans' criticism by asking if Democrats were working to take away guns.

On Friday, high-level calls took place between the Justice Department and Capitol Hill about background checks, an official familiar with the conversations said, with Attorney General Bill Barr -- who has also nudged Trump to support universal background checks -- sending a signal that talks had ground to a halt and prospects for presidential support for a background checks bill seemed to be dimming.

Senate Majority Leader Mitch McConnell has said he won't move on any gun measures until Trump spells out his position. After conversations with Trump last week, some lawmakers suggested his proposals would be coming imminently. But nothing has yet materialized, though officials said a plan would likely come this week.

Call with Democrats

In the Sunday phone call, which came at Pelosi and Schumer's request, the Democrats told him that anything short of the House-passed measure would be insufficient. The White House said the call was cordial, but said Trump offered no commitments on the House background checks bill.

Trump "instead indicated his interest in working to find a bipartisan legislative solution on appropriate responses to the issue of mass gun violence," a White House spokesman, Judd Deere, said.

The call came after Trump was briefed by advisers last Thursday about his options on gun control. Officials did not delve into specific legislative details and Trump did not appear interested in some of the nitty-gritty of how each proposal would work, a person familiar with the briefing said said.

Options the White House is considering include a phone application connected to the National Instant Criminal Background Checks (NICS). The app would be used for background checks during private sales and not ones involving commercial dealers, two sources familiar with the plans said.

The proposal wasn't finalized and is still awaiting sign-off from the President, the sources said.

Currently, there are no federally mandated background checks for private sales. Gun rights and privacy advocates have already voiced concerns about such an app because they say it could become a de facto registry, and there are concerns over how secure the information would be.

The app idea is one in a roster of ideas being mulled by Trump as he comes under pressure to act on guns. Other proposals include allowing minors' records to be included in background check databases; alerting local authorities when someone fails a background check; and applying bigger penalties for straw purchases (when someone buys a gun for someone else).

The administration is also looking at measures that would help states implement so-called red flag laws, which would remove weapons from people deemed at risk, and expediting the death penalty for convicted mass shooters.