The Blue Dog Democrats, AKA the Blue Dog Coalition, is a group of Democratic congressmen who work together to bring the Democratic party back towards the center of the political spectrum. Aside from being centrist, they are also well known for supporting protectionist policies, pay-go policies, and "individual responsibility" (i.e. less social welfare).
In recent years the Blue Dogs have numbered from about 30 to 50 individuals, plenty enough to make the Republicans happy. They tend to come from conservative districts, and often go against the Democratic grain. They have had disagreements with the Democratic Congressional Campaign Committee and Democratic Leadership Council, and love to bask in the glow of bipartisanship. There has certainly been some sore feelings within the Democratic party, with some liberal Democrats labeling some of the Blue Dogs as 'Bush Dogs' -- referring to the rather un-Democratic support that some Blue Dogs gave to president Bush in voting for war funds and warrantless wiretapping powers.
But that is not to say that all Blue Dogs are closet Republicans. One of the biggest issues for Blue Dogs is pay-go funding -- pay-as-you-go budgeting, where any big spending bills should be counterbalanced by big spending cuts or tax hikes. Republicans are well known as big spenders, particularly now that we have an expensive war to fund. Blue Dogs would want to pay for this directly, rather then run up a large national debt. Sadly, the Republican party does not seem to see the value in this. This sort of balanced spending is something that many Democrats would support, but somehow it has become a hallmark of the Blue Dogs in particular.
The Blue Dogs' website* claims that their name comes from a series of paintings done by the Cajun artist, George Rodrigue. Apparently the first meetings of what became the Blue Dog Coalition were held in the offices of the Louisiana representatives, Rep. Billy Tauzin and Rep. Jimmy Hayes. Both representatives had Rodrigue's paintings hanging on the walls of their offices, and the members took their name from these works of art. They were most likely influenced by the phrase Yellow Dog Democrat, a Democrat that would vote for any Democratic candidate who ran for office, even if the candidate was a dog. Representative John Tanner (from Tennessee) was quoted as saying that Blue Dogs were "...yellow dogs that have been choked by extremes in both political parties to the point they have turned blue."