A bill introduced by Senate Majority Leader Harry Reid (D-Nev.) would impose a 5.6 percent tax on earnings above $1 million per year, not the flat 5 percent tax some Democrats advertised on Wednesday.

That subtle difference is found in Reid's new bill, S. 1660. Another late change is that the so-called surtax on millionaires will take effect in 2013 — not 2012 as originally planned.

As reported Wednesday, Reid's bill abandons the "offsets" section of legislation proposed by President Obama and replaces it with the millionaire surtax. Obama's offsets included ending tax breaks for oil companies, families earning more than $250,000 per year, and corporate jet owners.

Reid reintroduced his bill as a new version of the American Jobs Act, which Senate Democrats are expected to take up as early as next week.