If new gun legislation doesn't pass in September, it won't get done before the 2020 election, sources involved in the talks between the White House and Capitol Hill tell Axios.

The bottom line: "It's September or bust," said a source involved in the discussions. "We'll either have everything ready for when Congress returns, drop it on the floor, vote on it and move on — or we blow it."

The state of play: The president genuinely wants to expand background checks, according to White House and Hill officials. He's directed the Domestic Policy Council and Office of Legislative Affairs to provide him with options for a reform package, these sources said.

As of now, Trump has expressed support for big, vague ideas — including tougher background checks and restrictions on firearms access to the mentally ill — but on the gun issue, consensus typically evaporates when lawmakers dive into the details.

It's also still unclear whether House Democrats, who have already passed a bill to extend background checks to all gun purchases, would support a slimmer package.

Behind the scenes: Rudy Giuliani says that he and Trump have discussed the need for "a bigger debate" over how much a psychiatrist is able to share from sessions with their patients.

"If a psychiatrist could disclose a little more, you might have been able to catch that guy," Giuliani said, referring to Sandy Hook gunman Adam Lanza, who had seen a psychiatrist before gunning down the elementary school.

you might have been able to catch that guy," Giuliani said, referring to Sandy Hook gunman Adam Lanza, who had seen a psychiatrist before gunning down the elementary school. Reality check: The Department of Health and Human Services sent a letter to doctors after the Aurora and Sandy Hook shootings specifically clarifying that they are allowed to release a patient's information "when you believe the patient presents a serious danger to himself or other people." It was also never reported that Lanza had revealed his intent to kill during his sessions with his psychiatrist.

The Department of Health and Human Services sent a letter to doctors after the Aurora and Sandy Hook shootings specifically clarifying that they are allowed to release a patient's information "when you believe the patient presents a serious danger to himself or other people." It was also never reported that Lanza had revealed his intent to kill during his sessions with his psychiatrist. "It would be really illuminating" to have psychiatrists testify about when their patients reveal a desire to kill people, Giuliani added.

to have psychiatrists testify about when their patients reveal a desire to kill people, Giuliani added. Giuliani also argued that the controversial New York "stop, question and frisk" policy is an effective deterrent for illegal gun owners.

New York "stop, question and frisk" policy is an effective deterrent for illegal gun owners. In 2013, a judge for the Southern District of New York ruled the policy violated the 14th Amendment's promise of equal protection.

Worth noting: It's unclear how serious these discussions were, and whether Trump agrees with Giuliani. Two senior White House officials say they haven't heard anything about bringing psychiatrists into the larger gun debate.

The big picture: The White House has been in listening mode over the past 2 weeks, including setting up staff sessions with aides to Sens. Joe Manchin (D-W.Va.), Pat Toomey (R-Pa.), Chris Murphy (D-Conn.) and others. The president and Ivanka Trump have also called around for advice on how to proceed.

As of now, the Manchin-Toomey bill, which would expand background checks to nearly all commercial firearm sales, is the jumping-off point.

But the bill, introduced in 2013 after the Sandy Hook shooting, previously failed after only getting the support of 4 Senate Republicans. Capitol Hill sources say they are waiting on White House officials to draft a "framework" showing the gun legislation that Trump has in mind.

Republicans who support gun control say that Trump is uniquely positioned — thanks to his alliance with the NRA — to give Republicans political cover to move to the left on guns.

Yes, but: Democrats familiar with the conversations and sources close to the president are deeply skeptical that any efforts will succeed.