The Democratic party already is. And has been for some 75 years. When I was looking for something else, I found this
Norman Thomas, the six-time Socialist Party candidate for U.S. President, said the following in a 1944 speech:
“The American people will never knowingly adopt socialism. But, under the name of ‘liberalism,’ they will adopt every fragment of the socialist program, until one day America will be a socialist nation, without knowing how it happened…. I no longer need to run as a Presidential Candidate for the Socialist Party. The Democratic Party has adopted our platform.”
And then I found this very interesting history of the Democrats at a site which intends to be “An Online Database of the left and its Agendas”.