According to Wikipedia, recess appointments last to the end of Congress's next session. That would be January 2018, right?
Anyway I think McConnell actually wants Obama to do this.
Assuming that Congress doesn't change its schedule, it would be until the end of the first session of the next Congress, which indeed would be January 2018. However, if Obama tried a recess appointment, it would be within the power of this Congress when it reconvenes on February 22 to immediately end the second session, start and then end a third session, and then begin a fourth session. Nothing in the Constitution says how long a session is, only that congress has to have at least one in each year. The recess power clause is one that needs to be revisited as both Congresses and Presidents have acted to make a mockery of what it was intended to be.
I don't believe this is true. The 20th Amendment says:
So yes, they can have as many sessions as they want, as long as they all start on January 3.