No, what happened was the Senators called Maryland Gov Larry Hogan who has command of the MD National Guard. He mobilized his troops but he needed permission from the Pentagon to move them into DC. He didn't receive authorization for over an hour while the Capitol was being overrun.
This is a separate issue from Mike Pence. This isn't about Pence vs. Senators; the question there is why wasn't Trump the one to make the call? Where was he in all of this in defending the Capitol. Reports are that he was reveling in the chaos, and making calls to Republican senators to lobby them to take more time and raise objections to the electoral certificates.