One of the Supreme Court Justices died recently, so the big news for the next few months will be picking a replacement.
What happens next depends on who is nominated. If it's a Democrat, the Republicans will try to block it. If it's a Republican, the Democrats will try to block it. It's possible that both parties will come together and filibuster the issue, so it's decided after the November Presidential election.
I could be wrong, but I think the record to replace a Supreme Court Justice is Lewis Powell, who retired June 26, 1987. He was replaced in February 18, 1988. That's almost eight months. It took so long, because two other people were rejected during that time. Wikipedia has more information on failed nominations.
The Supreme Court currently has four Republicans and four Democrats, but obviously, it's possible for Republicans to vote pro-Democrat, and vice versa. That's what happened with the gay marriage ruling last year.