Just what sort of pragmatist is Obama?
Elvin Lim thinks it is unhelpful to use the label.
Some, such as Ben Smith or Michael Gerson, think Obama's is a pragmatism of simple expediency, calling attention to an alleged lack of principle and willingness to compromise.
More plausibly, some locate his pragmatism in his desire to be post-partisan and anti-ideological. Both Cass Sunstein and Christopher Hayes discuss this possibility with Hayes leaning more toward the next possibility without firmly committing himself to it.
Still others, such as Mitchell Aboulafia, agree with Hayes about Obama's experimentalism, but go farther, identifying him as a philosophical pragmatist. Aboulafia even asserts in a recent post that Obama "knows" he is a philosophical pragmatist. I do not know what Obama knows.
What little bit I do know is here. For a full, well-worked account see Bart Schultz, "Obama's Political Philosophy: Pragmatism, Politics, and the University of Chicago," Philosophy of the Social Sciences 39 (2009): 127-173.