No, they did not. Trump's offer was made for the nation to hear, during the State of the Union. You should watch it again.
"The president picked a number for the wall, and I accepted it,” Schumer recalled in the midst of the shutdown. He had agreed to a significant sum of money for the wall—reported to be $20 billion, ... The White House ultimately rejected the offer, and later that night, Senate Democrats withheld their votes for a stopgap spending bill."
https://www.theatlantic.com/politics/archive/2018/01/democra...
1. http://azdailysun.com/news/national/govt-and-politics/a-time...
2. https://www.zerohedge.com/news/2018-01-23/schumer-withdraws-...
Just because Trump offered something doesn't mean Democrats didn't also offer something.
Further, Trump says a lot of things, he contradicts himself constantly, some times in the same sentence, so we can act like his statement in the state of the union was some ironclad agreement.
Yes, politicians often make statements for people to hear that are not in alignment with their preceding or following actions; Trump is not especially virtuous compared to other politicians in this regard. In fact, he's been frequently noted for the wide gulf between many of his public statements and not only his subsequent actions, but even his other public statements that are close in time.
https://fivethirtyeight.com/features/why-trump-isnt-taking-d...