What was going on behind the scenes, actually, is a story of Democratic manipulation of the rules process in the Senate. Paul is an outspoken opponent of the PATRIOT Act, which is up for renewal. We're in post-cloture time on the Act in the Senate, which is the time in which Senators are allowed to offer amendments. Harry Reid wants that clock to keep ticking during all hours of the day, including during lunch breaks and during Netanyahu's speech. Sen. Paul, who's more serious about legislating than the Democrat Majority Leader, wanted to continue debate on the legislation.
"Senator Paul wants to make sure that Harry Reid stands up to his end of the bargain on allowing amendments," his office's Communications Director said in a statement to Townhall.
The post-cloture time runs out at 11:45 pm tonight, and Paul wants to make the most of it. Democrats, who don't particularly care about legislating, want to be out to lunch while the clock ticks down. Sen. Paul wouldn't agree to a recess on what he obviously considers to be important legislation.
As Dave Weigel notes, there were other Senators who weren't at the Netanyahu speech as well. But because Sen. Paul was easy to find (on the floor of the Senate), it became a "protest." What's really going on here is, as usual, rules trickery and legislative apathy on the part of Democrat leadership.