As the Republican presidential nomination race heats up, President Obama’s national jobs tour is quickly becoming the electoral swing state tour in advance of the 2012 election.

Obama briefly brought his jobs bill fight back to Washington last week. But he resumes the road show Tuesday in Pittsburgh, the latest in a series of appearances in key battleground territory.

The president is scheduled to tour a training facility of the International Brotherhood of Electrical Workers and convene a meeting of the President’s Council on Jobs and Competitiveness. After making remarks at the training facility, Obama will head to Orlando for a fundraising event in the heart of another state that will be critical for him in 2012.

In unveiling his jobs plan to Congress last month, Obama pledged to sell it “to every corner of the country.” But the president has focused on swing states, including stops at universities in North Carolina and Virginia; a high school and interstate bridge in Ohio; a high school in Colorado and two fundraising events in Missouri. He’s also scheduled to appear in Michigan, North Carolina and Virginia over the next two weeks.

Obama carried each of these states except Missouri in 2008, and he lost the Show Me State by just 4,000 votes to John McCain.

Obama has chided his Republican adversaries for focusing on electoral politics during a period of deepening economic turmoil. Yet the president is using his $447 billion American Jobs Act as a political wedge to force Republicans to the negotiating table or risk being painted as a party that is unwilling to address the fiscal crisis.

Senior administration officials have said Obama will continue to push the jobs plan on the road through the end of the year.

In a memo released by the Obama 2012 campaign late Monday, senior strategist David Axelrod cited a Washington Post-ABC News poll last week that found 52 percent of Americans support the president’s jobs plan compared with 36 percent who oppose it.

“The more people know about the American Jobs Act; the more they hear the President talking about it; the more they want Congress to pass the plan,” Axelrod wrote.

On Tuesday, the Senate is scheduled to vote on the jobs package.

Last week, Senate Democrats proposed their own method to pay for the plan, proposing a 5.6 percent surtax on incomes of $1 million or more. Obama, who had proposed eliminating some tax loopholes and write-offs for people making more than $200,000 a year, has said he is comfortable with the new proposal.

However it is far from certain that the bill can pass the Senate, and House Republicans have already said the package would be dead on arrival.

“A faction in Washington may be content to wait until the next election to do anything,” Obama told his audience during a stop at North Carolina State University last month. “But I’ve got news for them: The next election is 14 months away. And the American people don’t have the luxury to wait that long,”

Republican leaders have said they would be willing to consider pieces of Obama’s plan, such as giving tax breaks to small businesses. The president has said he would sign any piece of the legislation that is approved and then demand that Congress send him the rest of his package or explain why they oppose it.

House Republicans have accused Obama of using the legislation as a campaign ploy.

“We’re legislating; he’s campaigning. It’s very disappointing,” House Speaker John A. Boehner (R-Ohio) said during a question-and-answer session last week at The Atlantic’s annual Washington Ideas Forum.

Obama’s visit to the Pittsburgh on Tuesday is the first of two trips this week to labor-heavy jurisdictions. He travels to Detroit on Friday to tour a General Motors factory with South Korean President Lee Myung-bak. The Obama administration is pushing Congress to approve free trade agreements with South Korea, Colombia and Panama.

Obama also has been courting organized labor, whose leaders had been critical of the president over the summer but have since been supportive of the jobs plan and applauded Obama’s bolder rhetoric.

Next week, Obama will travel to Asheville, N.C., where he will kick off a three-day bus tour of North Carolina and Virginia — his second trip to each of those states to tout his jobs proposal. He has previously appeared at North Carolina State University in Raleigh and at the University of Richmond.

In addition to the swing states, Obama also has made remarks about his jobs package during a West Coast fundraising trip to Seattle, San Jose, San Diego and Los Angeles. And last week, Obama spoke about his proposals at a Dallas-area community college, while also raising money for his re-election campaign in that city.