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The root of the fight is a battle between competing philosophies: Republicans, who say keeping tax rates on investment income low promotes more investment and savings, and Democrats, who say the experience of the Bush years shows little benefit from those low rates, but led to diminished fairness.

“In 2001 and 2003, the wealthiest Americans received two huge new tax cuts. We were told these tax cuts would lead to faster job growth. Instead, we got the slowest job growth in half a century, and the typical American family actually saw its income fall,” Mr. Obama said in his weekly radio address Saturday.

Small-business advocates say the proposed tax would sting.

“We’re much more interested in tax laws that impact the 22 million self-employed Americans who aren’t household names but who create a whole lot more jobs than Mr. Buffett,” said Kristie Arslan, president of the National Association for the Self-Employed.

She called for action on a broader tax overhaul that would simplify many of the credits available to small businesses and the self-employed.

At this point, the Buffett rule raises more questions than answers.

For starters, its effect on the deficit is subject to a huge degree of uncertainty. The Joint Committee on Taxation, which scores the effects of all tax bills in Congress, said that under current laws, the proposal would produce $47 billion more in revenue over the next decade - less than 1 percent of the additional deficits Mr. Obama’s budget would deliver during that time.

If the Bush-era tax cuts are extended, the tax bites more deeply - to the tune of $162 billion over 10 years, according to Mr. Whitehouse’s office.

About 89,000 people would be subject to the full 30 percent minimum, while another 134,000 would be in the phase-in range between $1 million and $2 million in income.