GOLDEN, Colo. — Mitt Romney promised Thursday that his economic program will create 12 million new jobs in the next four years, and likened President Barack Obama to a "dog trying to chase its tail" when it comes to strengthening the sluggish recovery.

Firing back instantly, Obama said his rival favors "trickle-down fairy dust" that has failed to fix the economy in the past, and unleashed a new television ad with a scathing summation of Romney's tax plans: "He pays less. You pay more."

The two men campaigned in battleground states hundreds of miles apart, the incumbent in Florida, his challenger in Colorado, both on a mission to convert undecided voters to their side in a race dominated by the economy.

For Romney, the day meant a return to domestic campaigning after a weeklong overseas trip. Aides say he intends to disclose a vice presidential pick before the Republican National Convention opens on Aug. 27 in Tampa, but the former Massachusetts governor gave no indication during the day that he has made a decision.

Instead, he unveiled what aides called Romney's plan for more jobs and more take-home pay, coupled with a self-generated report card that said Massachusetts enjoyed better economic times when he was governor than the nation has under Obama.

In remarks in Golden, Colo., he said his economic policies would lead to creation of 12 million jobs over the first four years, and help make North America energy-independent, a pledge that aides said included Canada and Mexico as well as the United States.

Romney pledged expanded international trade, particularly with Latin America, and vowed to confront China over its own policies. "I'm finally going to sit down with the Chinese and they're going to understand that if they cheat there are going to be consequences, because we're not going to let them walk all over us," the former Massachusetts governor said.

He said he would help small business owners, improve the education system and cut spending to reduce the deficit, but he offered relatively few specifics.

Romney has previously he wants to extend the tax cuts due to expire on Dec. 31 and grant a new 20 percent cut in tax rates in addition to stimulate growth. He has also said he will reverse some of Obama's proposed defense cuts, and simultaneously reduce spending on other programs in a way that deficits would gradually subside.

But he has so far refused to identify which existing tax breaks he would curtail to accomplish his goals, and generally avoided naming individual programs he wants to cut or eliminate.

In his remarks during the day, Romney said he wants federal education funds that aid the disadvantaged and disabled to be tied to the student rather than flow to school districts, as is now the case. But he did not specify how much he would cut from them to achieve his goal of reducing federal deficits.

He also criticized Obama for signing legislation that cut $500 billion from Medicare over a decade. But he didn't say whether he would restore the funds, and he has spoken favorably in the past of a House-passed budget that left the reductions in place.

In his remarks, Romney said Democrats have a different view. "They think we should just raise taxes. ...The problem is when you raise taxes you lower growth," he said.

Obama's approach is "like a dog trying to chase its tail, you just don't ever get there," he added. "So the right answer is not to raise taxes. The right answer is to cut taxes and cut spending."

Obama and other Democrats support extending existing tax cuts except for individuals making more than $200,000 a year and couples with incomes over $250,000 — and their disagreement with Romney and the Republicans on this point has emerged as arguably the most fundamental one of the campaign.

It's an argument that Obama seems eager to have — using campaign appearances and paid television advertising to do so.

For the second day in a row, Obama cited a study by the nonpartisan Tax Policy Center that says Romney and other millionaires would receive a tax cut of approximately $250,000 a year if the former Massachusetts governor gets his way.

"This analysis also found that if Gov. Romney wants to keep his word" about reducing deficits, "the average middle-class family with children would be stuck with a tax increase of more than $2,000," he added.

The president's new campaign ad was delivering the same highly personalized message. It says that Romney has paid a lower proportion of his income in taxes than many people of lesser means and adds:

"He pays less, you pay more," the ad says.

Romney's personal wealth has been estimated as high as $250 million, but he has not so far made public any detailed disclosure of his holdings. His aides have sought to dismiss the report as a partisan attack by former aides to the president.

But Obama, picking up on what his own campaign staff said on Wednesday, told an audience in Orlando, Fla., that the Tax Policy Center was headed by a former aide to President George W. Bush.

Romney too rolled out a new ad, giving a less-than-warm welcome to Obama on a day Air Force One touched down in Florida. It notes that the state still suffers from high unemployment, record home foreclosures and an increase in poverty.

"Barack Obama: What a disappointment," it says.

Associated Press writers Beth Fouhy in New York and Philip Elliott in Washington contributed to this report.