You think Chucky Schumer wouldn't have pulled the same stunt if Trump tried that, and promptly insisted that the U.S. Senate chamber WON'T be hosting a SOTU address because it would be "inappropriate" during a government shutdown? Heck, it would be "inappropriate" regardless, because there aren't enough seats in the Senate chamber to host a joint session of Congress, that's why joint sessions are always held in the House chamber. You simply couldn't pack hundreds of politicians, guests, and media figures into the Senate chamber.
There's a simple solution to this where Trump could have saved face. Prior to 1913, the standard procedure for a SOTU address was to send it as a written message to Congress. (and the "abolish the 17th amendment" crowd claims ANYTHING and everything Woodrow Wilson started in 1913 is AUTOMATICALLY evil, so presumably giving SOTU speeches before Congress is evil, too) Furthermore, THREE times in history (1945, 1956, 1973) the SOTU was delivered as a written message to Congress, followed by a public address by the President, summarizing to the American people what his goals for Congress are.
Trump should have just delivered his SOTU text to Congress on the day the speech was scheduled, and then promptly followed it up with a public address from the oval office a few hours later, where he used the bully pulpit to make his case directly to the voters. As an added bonus, the RATS would probably be blindsided by that and not have time to do the traditional prepared "Democratic response", and there wouldn't be all that annoying media coverage of various leftist figureheads the RATs invited to the SOTU address, like having some "trangendered" individual in the audience looking all sad and crestfallen as the media gleefully zooms in on a camera while Trump is speaking.
Chuckles has NO say-so in the Senate; the Turtle does.
This would’ve been my preferred response as well.