Try this link to an audio clip of a Danish speaker pronouncing the word "Rasmussen".
If link doesn't work, try this URL:
http://www.forvo.com/word/rasmussen/#da
Of course what matters is how Mr. Rasmussen (who I would guess is American-born) chooses to pronounce his name.
I could be wrong, but if memory serves, I believe he was asked that question on air at least once. Iirc his answer was "RASS mussen." But he said he didn't mind if people mispronounced it.
I love the way Hispanic Gals Roll the R when they say my name!