Not true. What is closed are certain departments of the Executive Branch. The Legislative Branch is open for business, and congressmen and senators are being paid. On January 3, the new House is sworn in, takes office and can do what it pleases.
Wont government employed Dems be happy to go without pay while the Dems in the House concentrate on hurting Trump not on getting the shutdown solved. That should really show them how much those creeps they elected care about them.
Except, it seems, the President can tell them to go home until needed.