I learned of this from a listener this morning while interviewing Senator Ron Johnson live on the show. I informed Johnson of it and he told me his office continued to run, albeit with a skeleton crew. I checked various U.S. Senate(democratic) websites. Harry Reid's, Dick Durbin's and Joe Manchin's do not have a statement that their offices are closed. North Dakota Democrat Heidi Heitkmap's web page has a message almost identical to Baldwin's. Interesting they didn't have a party-wide plan for this.
But what we do know is Baldwin was okay with using the shutdown as a silly excuse not to serve her constitutents and Ron Johnson was not.