[The Sons of Liberty]

Does the Senate chamber have the capacity to accommodate both houses of Congress for the SOTU?

Schedule it, and when the time arrive have the Sergeant at Arms bar all dems, "for security reasons". There'll be enough room.

[Dilbert San Diego]

The fire marshal could also ban entrance for most to the Senate. There are only 100 seats on the Senate floor, plus a certain number in the gallery.