The people most imminently in danger in that case, as I understand it, were staff in the Speakers Lobby, not members or the Vice President, who were in the chambers.

But as I understand the timeline, the attack, with defenders just on the other side with guns drawn and prepared to fire, on the doors to at least one of the chambers also were ongoing before members had been evacuated from the floor by another exit, so the incident at the Speakers Lobby came very close to being repeated where members were more immediately at risk.