The Florida seat has been vacant for 20 months and is categorized as a judicial emergency. Rubio put Thomas forward, back in 2012, then backtracked, refusing to provide a "blue slip" to the Judiciary Committee to advance the nomination. The North Carolina seat has been vacant since January 1, 2006, making it the longest-running vacancy in the federal judiciary. Obama put forward Jennifer May-Parker last summer initially with Burr's blessing. That's changed.
In a July 2009 letter to the White House, a copy of which was obtained by The Huffington Post, Burr recommended May-Parker for the slot and described her as having "the requisite qualifications to serve with distinction."Blue slips are a senate tradition but not a rule. In his tenure as chair of the committee, Sen. Patrick Leahy (D-VT) has upheld this tradition. His predecessor, Orrin Hatch (R-UT) ignored it. As a result of this opposition, the White House has given up and is not renominating Thomas, who would have been the first openly gay African American to serve on the federal bench. It's not yet clear whether May-Parker will be renominated.
Obama formally submitted her nomination to the Senate in June 2013. But May-Parker hasn’t moved since because Burr is withholding his "blue slip" to the Senate Judiciary Committee—a de-facto rule in the committee that allows a senator to advance or block a nominee for his or her home state. Fellow North Carolina Sen. Kay Hagan (D) has submitted her blue slip.
Some of that could depend on whether Senate Judiciary Democrats and President Obama decide to continue this fight. They've eliminated the filibuster for these nominees, but if there's going to be continued obstruction—and that's all this is—from Republicans who refuse to allow nominees even to get to committee, filibuster reform was a hollow victory.