Well, about 300 million people, but less than 100 million taxpayers. About 130 million workers in the US [1], of whom about 30% have a negative income tax rate[2]. Doesn't completely change your point, since less than half of Finland's population works as well[3], but I thought it worth mentioning.
Just because you have a zero or negative federal income tax rate doesn't mean you don't pay any taxes in the US. These people are still paying 7.65% payroll taxes on that income, sales tax, property tax, and the seemingly endless list of other taxes and government imposed fees we all pay on many other services. Since most social welfare programs are funded by a combination of federal and state taxes I don't think the number of people paying federal income tax is meaningful one way or the other.
"The employment rate of employed persons between 15 and 64-year-olds in April was 68.7 per cent, which was 0.2 percentage points higher than a year earlier. Employment rate for men fell from the previous year to April by 0.1 percentage points to 68.6 per cent. The female employment rate increased by 0.6 percentage points to 68.8 per cent. For seasonal and random variation, the trend was 68.7 percent."
[1] http://www.ritholtz.com/blog/2011/05/employed-persons-1999-2...
[2] http://www.washingtonpost.com/blogs/wonkblog/wp/2012/09/18/w...
[3] http://www.tradingeconomics.com/finland/employed-persons