WASHINGTON — Mitt Romney's Republicans charged President Barack Obama with "class warfare" Thursday in what is shaping up as a brutal battle for the White House, as both sides race to lasso votes of middle-class Americans.

The White House thrust back, accusing Romney of being "out of step with American values."

With Romney emerging as the inevitable Republican nominee to face Obama in the November election, his team is launching a counter-offensive against the president's push for higher taxes and what they say is a failure to initiate policies that would create jobs and speed up an economic recovery.

Former New Hampshire governor John Sununu, who plays the role of a top attack dog for Romney, said Obama's support for the so-called Buffett rule on the wealthiest Americans shows he is willing to institute taxes "designed to be punitive" on the rich while ignoring broader economic imperatives.

It is "a class warfare agenda that President Obama seems to be embarking on in this campaign," Sununu told reporters on a conference call.

The Buffett tax, named after billionaire US investor Warren Buffett who supports increasing taxes on the wealthy by ending loopholes imposed by former president George W. Bush, has little chance of passing in Congress next week.

Obama has begun the narrative that Republicans are more interested in lining gold-filled pockets than in helping working-class Americans.

"We now know who our opponent is," Obama said about Romney, in an email Thursday to potential campaign donors.

"He would shower billionaires with more huge tax breaks... starve investments in clean energy research, and make it harder for students to afford to go to college," he added.

Romney is hammering away at the Buffett rule, with his economic policy adviser Kevin Hassett calling it a "gussied-up" and politically motivated capital gains tax hike that will have little impact on soaring US debt.

The White House in return dispatched Vice President Joe Biden to the battleground state of New Hampshire, bordering Massachusetts where Romney once served as governor, to urge voters not to support "a system that's rigged" for the rich.

"We're not supposed to have a system with one set of rules for the wealthy and one set of rules for everyone else," Biden said in the town of Exeter.

Biden, in his fourth in a series of campaign speeches aimed at drawing distinctions between Obama's and Romney's economic visions, accused Romney of being "out of step with American values."

"They're good people but they have a fundamentally different economic philosophy than we do."

Biden warned against a return to policies, including tax breaks for the wealthy which Romney supports, laid out a decade ago by Obama's predecessor.

"Our economy faltered, the middle-class shrank, the poor got poorer, and ultimately the economy collapsed," Biden said. "And on whom did the economy collapse? It collapsed on you."

As if on cue, a baby in the crowd began to wail.

"I don't blame her for crying -- she is going to inherit it," Biden noted.

But he stressed that "this is not about class warfare, this is about math," as he argued that Americans can ill afford the $1 trillion cost over the next decade should Romney continue the tax cuts for the wealthy.

State Senator Jeb Bradley of New Hampshire, where the official motto is "Live Free or Die," criticized Biden for coming to "a state that has neither a broad-based income tax or a broad-based sales tax, with his message that it's time to raise taxes."

With their incomes increasingly stretched, New Hampshire families "don't want President Obama and Vice President Biden reaching deeper into their pockets," Bradley said.