Is the phrase "blind someone with science" understood or used in America?

Solution 1:

The expression appears to be mainly a British one; according to Ngram the only evidence of its usage is in BrE. Its origin predates the 1982 song which probably made the expression more popular. Here is an earlier example from 1947:

From: Failure of the Left, A Plea for a New Liberalism (1947)

• ... he is dreaming in terms of classes and class exploitation : his references to the mundane world are merely there to blind with science the proselyte who will not take his religion without evidence of a sort. When one contemplates the actual ...

According to The Concise New Partridge Dictionary of Slang and Unconventional English the expression "blind with science" first appeared in 1937 in Australia and in 1943 in UK.

Solution 2:

While I have only ever heard it used in the above mentioned song I have been familiar with the phrase my whole life. A similar phrase that I have heard used is to "baffle'em with bullshit" which is an abbreviated version of

“If you can't dazzle them with brilliance, baffle them with bullshit.” ― W.C. Fields