People who've tried to make the argument that there's no U.S. law saying they have to pay income taxes have been overruled by U.S. courts and sent to prison. No matter what argument was tried, the courts dismissed such cases as frivolous. To date I've never heard of anyone who succeeded with this argument in the long run. So whether there is a legitimate law or not, the courts certainly behave as if there is.
Here's an extensive FAQ about the "Tax Protester" arguments, how the courts have officially responded, and who ended up being sent to jail:
Tax Protester FAQ
For some general background, check out these Wikipedia entries:
Tax protester arguments - Wikipedia, the free encyclopedia Tax protester - Wikipedia, the free encyclopedia Tax avoidance and tax evasion - Wikipedia, the free encyclopedia
And here's a nice entry on Irwin Schiff, a prominent tax protester who repeatedly claimed there was no law compelling him to pay income taxes. Schiff won't be out of prison until 2016:
Irwin Schiff - Wikipedia, the free encyclopedia