The current Social Security Act has it origins in legislation introduced in January 1935 and passed by Congress later that year and signed into law by FDR in August.
For the record, and in the interest of historical accuracy, the vote on the 1935 SSA was pretty bi-partisan in that a majority of both parties' members voted in favor:
In the House: 372 Yeas (284 Democrats/81 repubs) v. 33 nays (15 Democrats/15 repubs)
In the Senate: 77 Yeas (60 Democrats/16 repugs) v. 7 nays (1 Democrat/6 repubs)
http://www.ssa.gov/history/tally.html