What Happens on June 1?

...when Patriot Act provisions expire, including the infamous 215 metadata program?

If we are lucky, not a lot, at least not right away.  Big terrorist operations take a few months to plan and potential attackers probably won't believe the US will do something this dumb to itself until it actually happens.  A lone wolf may feel emboldened, but organized groups will initially be cautious. 

After a week or so, potential attackers will probably look for ways they can exploit newly unsurveilled space for operational advantage.  Risk will increase steadily once they get over their shock, and then plateau two or three months out (when they've presumably adjusted their operations to reduced surveillance).  How much risk increases will depend on whether the USG can compensate for the lost collection and whether attackers find ways to gain advantage.

All the propaganda about how this kind of collection "never stopped an attack" is divorced from reality.  It is the the totality of collection that reduced risk.  Reduce collection and risk increases.  How much is unclear, and Americans may be willing to trade a small increase in risk for less government surveillance.  215 is probably the least valuable program, and ending it creates the least risk, but ending it is not risk free. 

Adding some privacy advocates to the Foreign Intelligence Surveillance Court will also increase risk.  We don't do this for any other kind of warrant process, and it will add delays.  One of the problems with FISC that led to the 9/11 success (for the other side) was the slowness of its processes.  Adding privacy advocates will return us to the bad old days of FISA.  It's also insulting to the judges. 

Privacy itself will not increase.  The privacy battle was lost years ago when extracting your personal data became the business model of the internet.  Americans have far less privacy than they did in 1995 and NSA has nothing to do with this.   There are several ironies in this situation, not the least being that NSA collection operated under far more rules than private sector or foreign government collection, and many of the immense private sector databases are likely accessible to foreign governments (if they decide they can use them). 

Senators Feinstein and Burr are each coming up with new bills to try and beat the clock and get 60 votes.  The most frightening part of this episode is its implications for constitutional government.  The drafters of the Constitution chose simple majority as the basis for decision making.  They did this because it was the inability to make legislative decisions that made the Continental Congress (the Republic's predecessor) unworkable.  If a majority in Congress support passage, the idea was that the bill should pass without the need for consensus or super majorities.  Anything else guarantees gridlock.