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 Romney favors “trickle-down fairy dust” that has not fixed 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, Obama in Florida, Romney in Colorado, both on a mission to convert undecided voters to their side in a race dominated by the economy and unemployment.

For Romney, the day meant a return to domestic campaigning after a weeklong overseas trip. Aides said he intends to disclose a vice presidential pick before the Republican National Convention opens on Aug. 27 in Tampa, but he told reporters “I’ve got nothing to give you” by way of information on his decision.

Instead, he unveiled what aides called his plan for more jobs and more take-home pay, backed by an eight-page paper arguing that the economic stimulus and other policies backed by Obama “exacerbated the economy’s structural problems and weakened the recovery. ... At the present rate of job creation, the nation will never return to full employment,” it said, on the eve of the release of the government’s report on July joblessness.

Following the release of the jobs report today, Obama planned to use the backdrop of the White House and surround himself with families who would benefit from the election-year middle-class tax cut he is pushing Congress to adopt.

In remarks in Golden, Colo., Romney said his economic policies would lead to the creation of 12 million jobs in the four years of his term, if he is elected, 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 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,” he 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 previously has said he wants to extend the tax cuts due to expire on Dec. 31 and grant a new, 20 percent cut in tax rates, 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.

He so far has 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.