There's no need to "grab the floor." All a senator need to to block progress is object to a unanimous consent request to conclude debate and vote on the amendment, the bill, the motion, or whatever it is that isn't otherwise subjected to a time limit for consideration.
We can argue all day about how the thing works. The fact is we are screwed , blued and tattooed.
Thank you! I hoped someone would hop in and set me straight if I was off base.