Although they still talk about it on-camera as an inquiry, top House Democrats see the actual impeachment of President Trump as increasingly inevitable.

• "The train has left the station," a senior leadership aide said, who thinks it's likely but not certain that Trump will become the third president to be impeached.
• Another aide, expressing more certainty than some others, tells me: "There's no going back."
• Rep. Gerry Connolly (D-Va.), reflecting the views of several members we talked to, said he thinks impeachment will happen by the end of the year: "My hope is it is expeditious. I don't want the clock to run out."

Why it matters: With that, House Speaker Nancy Pelosi faces a new conundrum: how to keep Democrats' other priorities from deteriorating amid an investigation of President Trump's dealings with Ukraine that could overshadow everything else.

• Several lawmakers have privately told Axios they never expected Congress to pass meaningful legislation before the 2020 elections.
• But Republicans will try to blame Pelosi for gridlock on the Hill, and they tell me they plan to use the same playbook on Pelosi as the one she crafted just a few weeks ago — demonizing Mitch McConnell as Washington's greatest obstructionist.

Behind the scenes: Pelosi's team developed a fall plan to escalate Dems' anti-McConnell messaging, with the goal of painting him as the party's prime antagonist blocking meaningful legislation.

• But those plans were blown up by the stunning news reports about Trump and Ukraine, and the moderate Democrats Pelosi had tried to protect began jumping aboard the impeachment train.
• Pelosi knew she had to formally launch impeachment proceedings or risk losing control of the caucus, sources familiar with her decision tell Axios.
• "The votes were there," a senior Dem congressional aide said. "If she didn’t proceed, her speakership would be over. ... And now there's no going back. We have to impeach him."

Republicans are eager to accuse Pelosi of failing to make progress on gun reform, the USMCA trade agreement and drug pricing.

• "This Dem-led House has managed to accomplish nothing of substance," a Trump official said. "And now that they’re going down this path of impeachment, they're going to be even more distracted. ... You bet that we're going to make sure voters are constantly reminded of this."
• “The NRA are probably the happiest people in Washington,” a former White House official said, adding that this will make it harder for Dems to blame Trump for inaction on gun regulation.

The bottom line: Pelosi has relentlessly reminded her House colleagues that Democrats regained the majority in 2018 by focusing on the issues, not by bashing Trump.

Officials are trying to carry out President Trump's months-old directive demanding that sponsors of immigrants pay the government for the costs when those immigrants used certain public benefits.

• But to tabulate that, they have to go through a cave in Missouri.

The bottom line: The majority of those immigration files — including sponsors' information — are located on physical sheets of paper often stored in a large, underground facility in Kansas City's limestone caves, multiple current and former government officials tell Axios' Stef Kight.

• "The cave stores more than 20 million immigration files, and we add 1.5 million new files every year," a U.S. Citizenship and Immigration Services (USCIS) Facebook post from 2014 says.

State of play: An interagency working group has had monthly calls with the White House to work out a system, an administration official tells Axios. But it's proved a complicated — if not impossible — task.

• "An alien's file could be hundreds of pages long," the official said. "It’s almost comical."

USCIS' former chief counsel, Ur Jaddou, said the agency has databases with some immigrant data points, and it has digitized a handful of forms — but there is no simple way to find an immigrant's sponsor.

• Family-based visas — one of the most common visas requiring sponsors — are handled entirely on paper, another former USCIS official said.

The response: A spokesperson said USCIS is continuing to work on digitizing records.

• Agencies have until Nov. 19 to come up with a solution.

President Trump’s decision to release the contents of his July call with Ukraine’s Volodymyr Zelensky has set a precedent his administration will have trouble containing, Axios' Dave Lawler writes.

Why it matters: Nicholas Burns, former undersecretary of state to George W. Bush, tells Axios that administrations try to keep presidential calls with foreign leaders confidential because "you want to preserve the ability to work with these people and you don’t want to embarrass them."

• Still, Burns thinks Trump’s calls with foreign leaders should be examined in an impeachment inquiry “because that constitutional imperative supersedes confidentiality with foreign leaders.”
• "Other world leaders are going to be extremely cautious in their conversations with him," Burns adds. "You'll never know if you’re going to find those conversations on the front page of the New York Times, or on Axios."

The impact: The Wall Street Journal reported that in addition to Trump’s call with Zelensky, his conversations with Russian and Saudi Arabian leaders were also hidden on the secret national security system "now central to the impeachment probe.”

• The Kremlin is warning against releasing transcripts of Trump’s calls with Vladimir Putin.
• But House Intel Chairman Adam Schiff told NBC's "Meet the Press" that he will push for memos from Trump's calls with other world leaders, including Putin.

Gérard Araud, who was the French ambassador to the U.S. until April, says seasoned world leaders were already far more cautious in their phone calls with Trump than Zelensky, who embarrassingly saw his criticism of German Chancellor Angela Merkel and flattery of Trump exposed.

• “When [French President Emmanuel] Macron was talking, he was talking about a precise topic," Araud says. "I have never had a paper where he was criticizing another head of state. He was not playing this game. Even if Trump was trying to, he was not."
• “It’s a small club,” Araud adds, noting that world leaders must worry not only about leaks, but also about what their foreign counterparts will tell one another.

Meanwhile, Susan Rice, President Barack Obama's former national security adviser, said in an interview Friday with Axios' Margaret Talev that there's a case for Congress to have access to more transcripts from Trump's conversations with foreign leaders.

• "In normal times, there is utility in the communications between foreign leaders having a measure of confidentiality; these are not normal times," Rice said.
• "I care more about what we don't yet know about what the president of the United States has done behind closed doors that run counter to U.S. national interests."

Tom Bossert, who was forced out last year as President Trump's homeland security adviser, told George Stephanopoulos on "ABC This Week" that he was "deeply disturbed" by Trump's phone call with Ukraine's Zelensky.

• And while Bossert said he doesn't believe Trump was "pressuring" Zelensky, he warned that Trump could be in serious trouble: "It is a bad day and a bad week for the president and for this country if he is asking for political dirt on an opponent."
• Bossert added that he thinks Rudy Giuliani — who also made the rounds on the Sunday shows — is largely to blame.

Biden pushback: The Biden campaign sent a letter today to top TV executives asking them to no longer book Giuliani on their programs.

• Read a copy of the letter.

The House and Senate are on recess until Oct. 15.

However, the House committees investigating Trump have scheduled a series of depositions and a hearing this week:

• Wednesday: Former U.S. Ambassador to Ukraine Marie "Masha" Yovanovitch.
• Thursday: Kurt Volker, who resigned Friday as Trump's Ukraine envoy.
• Friday: Intelligence community inspector general Michael Atkinson, who handled the whistleblower complaint, will appear before the House Intelligence Committee behind closed doors.

President Trump's schedule, per a White House official:

• Monday: Trump will participate in an Armed Forces welcome ceremony for the new chairman of the Joint Chiefs of Staff, Gen. Mark Milley, at Joint Base Myer-Henderson Hall in Virginia.
• Trump will also have lunch with Mike Pence, and he'll participate in the swearing-in of Labor Secretary Eugene Scalia.
• Wednesday: Trump will meet and hold a joint press conference with the president of Finland.
• Thursday: Trump will deliver remarks and sign an executive order on Medicare in The Villages, a Trump-friendly retirement community in central Florida.
• Friday: Trump will speak at the conservative Young Black Leadership Summit.

Wednesday marks the anniversary of the gruesome murder and dismemberment of journalist Jamal Khashoggi at a Saudi consulate in Istanbul.

• The fallout: Saudi Crown Prince Mohammed bin Salman (MBS) — who the CIA and a UN investigator believe was behind the attack — is still reckoning with the global outrage, which is casting a dark shadow over campaigns to modernize the country and thrusting the kingdom's human rights abuses into the spotlight.
• But Trump and Pompeo continue to work closely with the kingdom, emphasizing the importance of the U.S-Saudi relationship.

Tonight: CBS' Norah O'Donnell interviews MBS on "60 Minutes."