According to the Constitution, the President can make appointments of ALL officials when the Senate is in recess.
The fix to that is simply not to go into recess.
If they truly want to oppose President Obama from placing a liberal to very liberal to totally whacked-out Leftist on the Supreme Court—to replace a well-known conservative, they have every right to do so, and the Constitution provides them with the tools to do so.
They can chose whether to go on recess—or not—anytime a majority so decides.
Right now, the majority is nominally* Republican. If they stick together, then they can effectively stop this president from making a non-conservative appointment.
* Nominally—and I think we have to watch McCain, Kirk, Collins, Heller, Hatch, Cronyn, Graham and Murkowski. They’re all either Liberals or bending over backwards to get along and not get a press beat-down.