I think they should take up the nomination and debate it endlessly. They could easily stretch this on for months.
Obama and the rabid Dems will demagogue this endlessly, but truly, no one really cares about it.
There is ample precedent for not approving the SCOTUS nomination of a lame duck president.
The Republicans are in total control of this entire process. There are but two things McConnell must do: 1) block any nomination from coming to the floor of the Senate, and 2) keep the Senate in session by not declaring it in recess (just as, I am absolutely certain, the Democrat leader would do if the situation was reversed). There is absolutely nothing the Democrat/Socialists can do except scream -- which, of course, they are very good at.
As Mark Levin said on Saturday, Justice Scalia's seat on the USSC must be defended.