The Note: Trump tears down the wall with Democrats, but is it a trap?

— -- THE TAKE with ABC News' Rick Klein

President Trump is claiming "no deal," but it sure sounds like he cut one – and that means a massive defining down of his signature border wall. The "Chuck and Nancy" show's run isn't over, it appears: The top Democrats in the House and Senate said they reached an agreement to legalize DACA recipients in exchange for border funding, details to come. Trump tweeted this morning that the wall "is already under construction in the form of new renovation of old and existing fences and walls" – an important tell, in that it gives him an enormous out. The deal many Democrats and some worried Republicans see coming into view gives in on DACA in exchange for something that falls far short of the "big beautiful wall" that Mexico was supposed to pay for. Trump, of course, will never admit that, and will say his wall is funded. But traps loom for both of the sides who enjoyed Chinese food at the White House Wednesday night. You can't play ball if both sides are busy playing each other.

BUDGET BATTLE FOCUSES ON EPA

Before Republicans have a shot at passing a tax overhaul, they need to pass a budget, and that debate is far from over. Not only do a number of Republicans want more cuts and a sneak peek at the tax plan before they vote on a budget, plenty of Democrats are still fighting against the budget cuts Republicans are proposing. For example, while Republicans largely balked at the 30 percent cut to the Environmental Protection Agency the White House initially suggested, the latest House budget still includes roughly a 5 percent cut to the agency. Many Democrats aren't celebrating that as some win. At a news conference in Washington Wednesday, federal employee union representatives warned of possible office closings if mission and personnel were rolled back at the EPA. They said they been told the administration was considering shuttering a lab in Houston of all places, which has been central to environmental monitoring post-Hurricane Harvey, ABC News' MaryAlice Parks writes.

WHAT YOU NEED TO KNOW TODAY

QUOTE OF THE DAY

"I don't think it was probably the best start." -- Former White House press secretary Sean Spicer to ABC's "Jimmy Kimmel Live" on defending Trump's inauguration crowd size.

NEED TO READ with ABC News' Paola Chavez

Treasury Secretary Mnuchin requested government jet for European honeymoon. Secretary Steven Mnuchin requested use of a government jet to take him and his wife on their honeymoon in Scotland, France and Italy earlier this summer, sparking an "inquiry" by the Treasury Department's Office of Inspector General, sources told ABC News. Officials familiar with the matter say the highly unusual ask for a U.S. Air Force jet, which according to an Air Force spokesman could cost roughly $25,000 per hour to operate, was put in writing by the secretary's office but eventually deemed unnecessary after further consideration by Treasury Department officials. http://abcn.ws/2wXWzlS

Democrats claim deal reached with Trump on some undocumented immigrants. President Trump and congressional Democrats agreed Wednesday night to work together on a legislative package to address the status of some undocumented immigrants. Democrats say the agreement would include protections for Dreamers and border security measures short of a border wall, a characterization disputed by the White House after the two-hour dinner. http://abcn.ws/2fksLpL

Here's what's in Bernie Sanders' "Medicare-for-all" bill. It was a big day on Capitol Hill for Sen. Bernie Sanders and the debate over health care policy in the United States. Surrounded by a dozen of his Democratic colleagues, nurses, doctors and patient advocates, the Vermont independent introduced the latest version of his health care bill Wednesday, a proposal he refers to as "Medicare-for-all." http://abcn.ws/2eWdXgl

Republicans make last-minute pitch for Obamacare repeal plan. It was a day of dueling health care plans on Capitol Hill. Sen. Lindsey Graham, R-S.C., who's leading the Republicans' last-minute effort to repeal and replace the 2010 Affordable Care Act, came out swinging against Sen. Bernie Sanders' proposal for what he calls "Medicare for all." http://abcn.ws/2eWvzsn

Americans "manipulated into believing that they're enemies," HUD Secretary Ben Carson says. Americans have "allowed themselves to be manipulated into believing they're enemies," Housing and Urban Development Secretary Ben Carson says, offering his explanation for the sharp divide exposed in last month's violent protests in Charlottesville, Virginia. "I think a lot of the Americans that get caught up in this are decent people but they've allowed themselves to be manipulated into believing that they're enemies and that they should hate each other, and that they should try to destroy each other, and this is exactly the wrong thing," Carson told ABC News' "Powerhouse Politics" podcast. http://abcn.ws/2h2KR30

North Korea crisis: Mnuchin suggests China trade cut-off on the table. Fox News

Trump FEMA nominee withdraws after NBC questions on falsified records. NBC News

Cruz on porn video "liked" on his Twitter account: "It was not me." CNN

The Note is a daily ABC News feature that highlights the key political moments of the day ahead. Please check back tomorrow for the latest.