$11k/month contracting in the US is very different from $11k salary in the US, let alone Europe.
~7.5% extra tax right off the top, versus salaried (employer usually pays that part for salaried employees, and it's not stated as being part of one's salary, ever) in addition to all the usual taxes.
Our version of a "public pension" is terrible, so you'll need some contributions to a 401K if you ever want to retire, and unlike someone salaried the employer won't be chipping in any extra above your salary (typical for salaried employees is some % of "matching" money for your contributions, so you put in 3% of salary and your employer puts in the same amount, above your salary). Then there's the fact that for any competitive goods (say, housing in a decent school district near where jobs exist) you're competing with people who are choosing not to save that money, so there's pressure on prices that wouldn't exist with a better compulsory pension system.
Health care for a family will probably run 1.5-2k/month without an employer chipping in, and still leave you exposed to $20k-$30k of risk per year ("out-of-pocket max") and spending another $500-$1,000/yr even in a good year.
Depending on your arrangement, you may have to deduct pay for any vacation or sick days taken. Take 30 working days out of that (not unusual for sick + vacation in Europe, if we're comparing to European total comp) and that's another ~10% of your annual pay gone.