(REUTERS) — Millionaires would pay a minimum 30 percent effective tax rate under a law introduced on Wednesday in the Senate with the backing of President Barack Obama and named after billionaire investor Warren Buffett.

Nicknamed the “Buffett Rule,” the tax bill reflects Democrat Obama’s bid ahead of November elections to highlight the sort of unfairness he says is represented by Buffett’s tax anomaly – that he pays a lower effective rate than his secretary does.

The “Paying a Fair Share Act of 2012,” introduced by Democratic Senator Sheldon Whitehouse, has almost no chance of passage this year as the Republican-controlled House of Representatives has sworn off tax increases.

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