"Impeachment is a very divisive approach to take and we shouldn't take it ... without the facts", she told host Joy Reid later in the interview, set to air Friday at 10 p.m. ET.
Among her entourage, a Palestinian-American comedian, Mo Amer, saw the map and added the Post-it, according to Buzzfeed News.
Financial Services Chairwoman Maxine Waters, a frequent target of Trump's ire, said of Tlaib comments: "I think what we need to do is have more attention on the President and the way that he speaks, the language that he uses".
Such progressives will be eager to push back against an administration they believe has abused its authority in the almost two years since Trump's inauguration.
Her spokesman, Denzel McCampbell, said in a statement that Tlaib, one of only two Muslim women in Congress, "was elected to shake up Washington" and will not stay silent.
"The congresswoman has the power of speech is hers", he said.
"You can't impeach somebody who's doing a great job", Trump told reporters at the White House on Friday.
The president also said that he did not recognize her name, saying, "This is a person I do not know, I assume she's new".
Shutdown restricting visits, cleaning at national parks
The Washington Post notes that the Trump administration initially kept most of the parks open with skeleton crews to enforce some of the rules.
As a clip of Michigan Democrat Rashida Tlaib's animated comments circulated widely on social media, Trump tartly dismissed the threat of impeachment on Twitter on Friday.
Hammill later tweeted a slightly different recap: "Speaker Pelosi made clear that today's meeting was about re-opening government, not impeachment".
Sherman and Green forced votes to impeach Trump in 2017 and 2018, but the Republican House blocked those resolutions twice, with the help of many Democrats who said the effort was premature.
A similar dynamic (righty House Republicans demanding the impossible in the face of a Democratic president and Senate) drove then-Speaker John Boehner into retirement a few years back.
"I think those kind of comments do not take us in the right direction", said Oversight Chairman Elijah Cummings of Maryland.
Virginia Rep. Gerry Connolly said the comments were just "red meat" for Tlaib's supporters.
"How was she going to stand up to the most radical-left elements of her party when they become unhinged?" "It doesn't reflect the caucus, and I'm sure upon reflection, she might choose other words to describe her feelings".