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Darrell West, the director of governance studies for the Brookings Institution, said the president’s speech reflects the deeply polarized political climate. General election candidates usually like to fuzz the differences between the parties and focus on appealing to centrist voters, he said.

“Both Romney and Obama have incentives to play to the base,” he said. “Each of them needs a very strong turnout from committed people.”

Because the unemployment rate is likely to remain at or above 8 percent for much of the year, Mr. Obama cannot claim to have resided over a full economic recovery. Instead, Mr. West said, he wants to take advantage of the tea party swinging Republicans to the right, accuse his opponent of extremism and avoid the election being cast as a referendum on him.

“If it’s a referendum on him, he loses,” Mr West said.

In his speech, Mr. Obama listed the areas where he said the Republicans’ budget would lead to cuts, ranging from education, environmental protections and clean energy incentives to national parks and crime-fighting money within the FBI.

He acknowledged that those cuts aren’t specified in the budget, but said those are the choices lawmakers will have to face, given the amount of government spending the GOP calls for.

“Perhaps they will never tell us where the knife will fall, but you can be sure that with cuts this deep, there is no secret plan or formula that will be able to protect the investments we need to help our economy grow,” he said. “This is not conjecture. I am not exaggerating. These are facts.”

By contrast, he said, wealthier Americans can afford a tax rise that would help continue funding all of those needs.

His own budget calls for tax rates on those in the highest tax brackets to return to the levels they were under President Clinton, and he also proposes a new “Buffett Rule” tax of a minimum tax rate on those making at least $1 million a year.

The tax is named after billionaire Warren Buffett, who has decried the fact that his investment income is taxed at a lower rate than the salary and wage income of his secretary.