The state of play: Byard's nomination had not been withdrawn as of Wednesday evening, per one administration official.

• But Trump has already made a decision to move forward with Gaynor, according to sources both inside and outside of the administration.
• Gaynor has served as the agency's acting administrator while Byard's nomination stalled in the Senate. The president was impressed with the way Gaynor handled Hurricane Dorian.

The backstory: Trump nominated Byard — the associate administrator for FEMA's Office of Response and Recovery — to lead the agency in February after former FEMA administrator Brock Long resigned amid an investigation into his personal use of government vehicles.

• Byard's nomination went through the Senate Homeland Security Committee (HSGAC) in June, but issues regarding a personal conflict later arose and have continued to hold up his nomination.
• Politico first reported that the White House was considering pulling Byard's nomination.

Worth noting: The nature of Byard's "personal issue," as several sources familiar describe it, is still unclear. Only a select few people — including Senate Homeland Security Chairman Ron Johnson and a small circle of administration officials — actually know.

Why it matters: The president was expected to say this week what, if any, gun control legislation he is prepared to support. Advocates were doubtful he would support expanded background checks because polling suggested it could hurt his standing with core supporters.

The memo, first reported by the Daily Caller and also obtained by Axios, suggests he may be open to background checks depending on feedback from Republican lawmakers.

• The memo talks about extending a background-check requirement "to all advertised commercial sales, including sales at gun shows."
• It would be consistent with the bipartisan Manchin-Toomey draft legislation.
• It would impose civil penalties for failure to keep necessary records.

Where it stands: The president has not said publicly whether he supports the proposal in the memo or is just shopping it. White House spokesman Hogan Gidley said Trump "has not signed off on anything yet" and said the memo is "not a White House document."

• Meanwhile, the head of the NRA's lobbying arm, Jason Ouimet, said that the memo is a "nonstarter," because "it burdens law-abiding gun owners while ignoring what actually matters: fixing the broken mental health system and the prosecution of violent criminals."

Read the memo:

Editor's note: This story has been updated with responses from the White House and the NRA.

Instead, Democrats once again showed their frustration at Trump's brazen strategy of simply refusing to cooperate with Democrats' probes.

• The White House prevented two former Trump aides, Rob Porter and Rick Dearborn, from testifying.
• Lewandowski, a former Trump campaign manager who's eyeing a Senate race in New Hampshire, was so unforthcoming that at one point, all he freely volunteered was that his favorite NFL team is the Patriots.
• "I will be as sincere in my answers as this committee is in its questions," Lewandowski said as the hearing began.

The big split: A division remains between Democrats who want to move toward impeachment regardless of how it plays politically — and those focused on preserving the House majority, and a broad enough public appeal to win the White House.

Several members on the committee tell Axios that despite personally supporting impeachment, they recognize Pelosi has a different job, and respect that she has to protect the caucus and the new majority.

• "There are differences about timing and whether we do it at all," Rep. Gerry Connolly, who serves on the House Oversight Committee and recently came out in support of impeachment, tells Axios. "But we can live with ambiguity and we're not going to be pushed into arbitrary deadlines."
• "The Speaker has to have the ability to see the entire field. She has to consider a lot of things I don't," Rep. Val Demings (D-Fla). said.
• "The Speaker is a pretty good person to measure her own barometer. She'll know when she needs to act or not act," said Rep. Steve Cohen (D-Tenn.).

In one victory for Democrats, Lewandowski confirmed as "accurate" the Mueller report's account that Trump had asked him to direct then-Attorney General Jeff Sessions to limit Mueller's investigation. Trump said that if Sessions would not meet with Lewandowski, Lewandowski should tell Sessions he was fired.

• Lewandowski never delivered the message. When Democrats asked if he "chickened out," Lewandowski said he took his kids to the beach instead. (AP)

Between the lines: Many Democrats still think there's an impeachment case to be made, but that investigations and court rulings need to run their course for months to come.

• "We can’t get this close to getting some answers and then say we’re going to move forward with impeachment without getting the answers,” a Dem leadership aide told Axios.
• "When we compile our record here in the Judiciary Committee, I believe it'll be so compelling that impeachment resolutions will flow naturally," said Rep. Hank Johnson (D-Ga.), a key questioner yesterday.

Go deeper: Corey Lewandowski stonewalls House Democrats in impeachment hearing