This doesn't answer your question about what proportion of your paycheck goes to welfare, but it discusses total "means-tested federal welfare" spending, which is huge.
http://globaleconomicanalysis.blogspot.com/2012/12/crazy-incentives-in-welfare-system.html
"According to data from the Congressional Research Service, cumulative spending on means-tested federal welfare programs, if converted into cash, would equal $167.65 per day per household living below the poverty level. By comparison, the median household income in 2011 of $50,054 equals $137.13 per day. Additionally, spending on federal welfare benefits, if converted into cash payments, equals enough to provide $30.60 per hour, 40 hours per week, to each household living below poverty. The median household hourly wage is $25.03. "
The 2nd chart in that article, about the welfare cliffs, is interesting. It's a chart from Pennsylvaniaâs secretary of Public Welfare showing that in many cases, people are getting so much welfare that to take a job would mean less income than they are getting from welfare.
"As the above chart â via Gary Alexander, Pennsylvaniaâs secretary of Public Welfare â shows, the single mom is better off earning gross income of $29,000 with $57,327 in net income and benefits than to earn gross income of $69,000 with net income & benefits of $57,045."
Just for the sake of balance, I want to point out that corporate and military welfare is just as bad or worse in terms of wasted money.