Harper introduced a separate bill in 2011 to end public financing for presidential campaigns and party conventions, using the roughly $200 million in savings for deficit reduction. It passed the House on a party-line vote.
Cantor's latest measure could put House Democrats in a difficult position if they still oppose ending public financing for campaigns and could now be attacked in campaign ads for voting against funding for autism research.
"Transforming welfare for politicians into efforts to eradicate this terrible disease is a much better reflection of our national prerogatives," Cole said. "This legislation is an example of how much can be accomplished by ending wasteful spending and redirecting those funds toward urgent national priorities like the need to combat autism."
The $200 million Cantor's proposal would restore is about 8 percent of the $1.6 billion cut from the NIH under sequestration.