The short of it is the Senate can stifle as many as it once by holding pro-forma (fake) sessions every 3 days during a recess. Also Obama's NLRB appointments are invalidated.
But what about other recess appointments in the future? The short answer is that it really will depend on which parties are in power. Right now Democrats control both the White House and the Senate. With the decision by Senate Democrats back in November to invoke the “nuclear option” – which allows them to confirm the president’s nominees with a simple majority – right now the president doesn’t need to use recess appointments to fill judgeships or senior positions in the executive branch. But that could change if the Republicans gain control of the Senate this November (a prospect that many believe is increasingly likely): a Republican Senate could not only block the president’s nominees, but prevent the president from making recess appointments by ensuring that it never recesses for more than a few days. And, of course, the shoe could be on the other foot if – after the 2016 elections — the Democrats were to control the Senate but lose the White House. So even if the president’s recess appointments power may not factor into many voters’ decision-making process, it certainly could hang in the balance in the next two elections.