Implies that if a woman were to suspend an aspirin between her knees, she would be unable to spread her legs without dropping the aspirin, thus, by keeping the aspirin suspended between her knees, she would be unable to engage in activities deemed sinful by crazy out-of-touch right wing nut jobs who wish to impose their religious will on the American public
Person 1:

"Hey! Did you see that Rick Santorum supporter Foster Friess on TV the other day? That nut job actually suggested that women should suspend an aspirin between the knees and use that as contraception!"

Person 2:
"Man, that guy is out of touch! I guess we can thank right wing nutters like those guys for paving the way to Obama's second term..."
by phroug2 February 17, 2012
To make some phenomenal gaffe or faux pas, similar to putting your foot in your mouth.
Man, I really put the aspirin between my knees yesterday. I told Jen that her new dress made her look fat.
by Two Hep Cats February 18, 2012