* Obama calls Republican budget a "Trojan horse"
* Says plan will end Medicare "as we know it"
* Republicans says attack is "unhinged"
By Alister Bull
WASHINGTON, April 3 (Reuters) - President Barack Obama accused Republicans on Tuesday of favoring the rich with a "radical" budget plan that focuses on cutting popular programs, which the White House sees as a potent vote winner for Democrats in this year's election.
In a week in which Mitt Romney is expected to extend his lead in the race for the Republican nomination to confront Obama in the Nov. 6 election, the president took aim at their new budget blueprint, calling it "thinly veiled social Darwinism."
In a withering attack, Obama painted his opponents as having veered sharply to the right as he sought to persuade voters that his own policies reflect America's traditional mainstream.
"This congressional Republican budget ... it's a Trojan horse. Disguised as deficit-reduction plan, it's really an attempt to impose a radical vision on our country," the president said.
"The Republicans running Congress right now have doubled down and proposed a budget so far to the right it makes the Contract with America look like the New Deal," Obama said.
The comparison of a 1994 Republican manifesto with the 1930s social programs of Democratic President Franklin Delano Roosevelt drew sharp pushback.
Representative Jeb Hensarling, a member of the House of Representatives' Republican leadership, called the remarks an "unhinged attack", while House Speaker John Boehner, the top Republican in Congress, said the speech showed Obama was more interested in campaigning than governing.
Acknowledging that the general election was heating up, Obama also offered a rare name-check of the Republican front-runner, noting in a speech that "one of my potential opponents, Governor Romney," had voiced hope he could sign a similar budget into law on day one of his presidency, if he won in November.
"He even called it marvelous, which is a word you don't often hear when it comes to describing a budget," said Obama, who laid out a laundry list of programs he warned would be savaged by Republican cuts, from education to healthcare.
"It is a bad idea and it will ultimately end Medicare as we know it," Obama said, tapping into fears of what might happen to the federal healthcare plan for the elderly which Democrats will play up in the election.
The partisan budget proposal, passed by House Republicans last week, would curb deficits by cutting spending while reforming the tax code. It would lower the top tax rates on individuals and corporations to 25 percent from the current 35 percent.
Republicans contend it is an answer to his spending policies, which they blame for record budget deficits on his watch, and said Obama's account of their goals was not fair.
"The president has resorted to distortions and partisan pot-shots, and recommitted himself to policies that have made our country's debt crisis worse," said Boehner.
The Republican budget proposal has no chance of passing the Democratic-controlled Senate. But White House officials said the goal of Obama's speech was to hammer home a message that if Republicans win in November, their budget is coming to America.
Stepping up the campaign against Romney, one of the richest men ever to seek the White House, Obama officials said the president will speak again on Friday at a conference on women in the economy, at which he is expected to slam Republicans again.
His remarks will also come on the same day the government is due to release its latest employment estimates. Forecasters polled by Reuters estimate payrolls grew by 203,000 in March, which would boost Obama's claim that the economy is healing.
A poll on Monday showed Obama was opening a large lead over Romney among women voters in key election swing states.
Senior Obama officials say they were not surprised by the poll's findings after recent remarks about birth control by Republican candidates on the campaign trail, which they said sounded like an echo from the 1950s, and were a clear turn-off for many young women.
Romney has said he would end federal funding for the Planned Parenthood women's health organization that provides abortion services and Rick Santorum, his chief rival for the Republican nomination, has called contraception morally wrong.
Romney hopes to all but wrap the race up this week by winning election contests in Wisconsin, Maryland and Washington D.C. He wants to pressure Santorum to stand aside and unite the Republican party with the goal of defeating Obama in November.
Pressing his priorities on raising taxes on the wealthy, protecting Medicare and defending the middle class, which he hopes will peel away blue collar voters from the Republicans, Obama said the House-passed budget would fundamentally change America, and not in a good way.
To discredit his opponents' approach to taxes and spending, Obama also invoked the widening wealth gap between the top 1 percent of U.S. earners and the rest of the nation, which last year helped galvanize a nationwide 'Occupy' protest movement.
The Republican budget plan caps discretionary spending on things like education and infrastructure and cuts spending on welfare programs for the poor including for food stamps and housing.
The Republican blueprint also proposes broad tax reform, including closing loopholes to raise revenue, while advocating a simplification in the tax code and lowering the top tax rate.