Per the official Marlins website, there is a deadline of Tuesday for getting a Beckett trade done:
The two clubs set a 48-hour deadline Sunday to work out a deal before Tuesday. It's unclear if that deadline is set in stone. One reason for the delay on Sunday was that Marlins owner Jeffrey Loria, who is in Europe, was not easily accessible. This is a unique trade because it is being negotiated by the owners of both clubs.
Texas owner Tom Hicks has had numerous discussions with Loria. The Rangers are eager to get the deal done because other teams have shown interest in Beckett. The source said the Rangers want to secure Beckett before the Red Sox get deeply involved.
Again, I'm not sure why Hicks would be handling the negotiations on this deal.