WASHINGTON — Although impeachment appears to be sucking the oxygen out of legislative progress on major issues, Connecticut’s Democratic senators insist negotiations on gun legislation remain ongoing and the White House has not shut the door on either expanded background checks or the “red flag” emergency restraining order.

“I have by no means given up hope,” said Sen. Richard Blumenthal, who along with Sen. Chris Murphy has been in the lead on guns among Senate Democrats. “Any time you’re dealing with gun-violence prevention, the path is always uphill. And it’s true we’re living in unprecedented and turbulent times. But that presents opportunities as well as challenges.”

And also they present a wild card: The National Rifle Association.

The NRA’s CEO, Wayne LaPierre, met with President Donald Trump to hear the president’s appeal for support amid House Democrats’ impeachment inquiry, and reportedly told Trump to “stop the games” on possibly favoring gun-control legislation, according to the New York Times. The NRA issued a statement calling the Times report “inaccurate.”

If true, Trump may be more inclined to halt his flirtation with Murphy, Blumenthal and others favoring expansion of background checks to private transactions, and a “red flag” law that would encourage states to adopt laws similar to the one Connecticut pioneered in 1999: Permitting police or family members to seek a judicial order to remove guns from possession of a troubled individual.

But Trump may be inclined to deal on guns as a way of diverting attention from the impeachment probe, sparked last week by a whistleblower’s report detailing Trump’s pressuring of Ukraine’s president for dirt that would damage former Vice President Joe Biden’s 2020 campaign.

In an appearance Monday on MSNBC’s “Morning Joe,” Murphy talked about receiving a call from an unidentified White House official on the day last week that the impeachment story burst wide open.

The official, Murphy said, expressed hope that Murphy’s stand in favor of opening an impeachment inquiry would not interfere with possible agreement on gun legislation.

“I told them of course I can walk and chew gum at same time,” Murphy said .”This is about life or death. (Such legislation would) save thousands of lives in this country. I frankly don’t care if that accrues a bit to a president in the middle of an impeachment inquiry.”

Blumenthal said Monday that he too received a call from a high-ranking White House official, whom he declined to name.

The official, Blumenthal said, expressed hope that Blumenthal’s “red-flag” proposal _ co-authored with Senate Judiciary Committee chairman Sen. Lindsey Graham, R-S.C., would remain on track despite an impeachment inquiry.

“We need to seize the moment no matter how long odds may be,” Blumenthal said. “I don’t want to sound Pollyanna-ish, but progress will never be made if we adopt the more negative viewpoint.”

Trump himself has offered little encouragement.

At a news conference in New York last week, he singled out Murphy as “so nice” in their negotiations on guns. But now, Murphy is “too busy wasting time on the witch hunt.”

For its part, the NRA is battered and bruised after a year or more of internal power struggles, declining membership and sagging revenues. And last week, the Democratic minority on the Senate Finance Committee issued a report detailing connections between Russia and the NRA that may implicate the group in tax and sanctions violations.

Blumenthal said he had talked to Republican senators who told him the NRA is “crumbling” and “a shadow of its former self.”

“The ground is shifting under the gun lobby’s feet,” Blumenthal said, citing conversations with gun owners during a weekend stop in Durham, Conn. “These are law-abiding hunters and recreation shooters who want no part in mass shootings and suicides.”

Blumenthal said he and Graham were close to producing a “red flag” measure, which would offer grants and other federal assistance to state to help them set up laws and enforcement mechanisms for ERPO’s _ Emergency Risk Protection Orders.

Attorney General William Barr has circulated a compromise on background checks, calling for such checks to be conducted on any transaction involving advertising or marketing of weapons. It would also create a class of licensed transfer agents who would conduct the background checks.

A spokesman for the Newtown-based National Shooting Sports Foundation, the gun industry’s main trade group, said it reviewed the proposal and found it wanting.

“We believe it is crucial to fix the background check system before it is expanded,” said the spokesman, Mark Oliva, citing NSSF-supported legislation that encouraged states to submit more records to the FBI’s National Instant Criminal Background Check System that would aid in disqualifying gun purchasers. “Our firearms retailers rely on this system to be accurate to ensure firearms are not sold to those who are prohibited persons.”