President Obama used this manufacturing hub — and important swing state — as the backdrop to draw a sharp distinction Wednesday with his Republican rivals over the economy, as both sides aim to frame the debate for the coming presidential race.

The day after House Republicans unveiled their budget proposal — which would cut more than $5 trillion out of the federal budget over the next decade and balance the budget by cutting domestic programs — the president touted some of the very programs that would come under the GOP axe.

Obama dismissed a House plan that “doubles down on trickle down,” giving tax cuts to wealthier Americans. And he boasted about the health of the U.S. economy, reiterating his message from the State of the Union in January that the recession is quickly becoming a distant memory.

“I’m also going to take a little credit,” Obama said during remarks at the City Club of Cleveland. “It was the result of decisions my administration made with some [Democratic] members of Congress who are here to prevent a second depression. A lot of those decisions were controversial.”

To a large extent, the economic fight will center on the question of whether Democrats’ support for more federal investment or Republicans’ backing for deeper tax cuts represent the best path for economic growth. And that debate will help determine who occupies the White House once Obama leaves office.

President Obama is captured on a cell phone as he greets people after speaking in Cleveland. (Tony Dejak/AP)

Speaking in the home state of House Speaker John A. Boehner (R), Obama noted that Boehner had repeatedly asked voters in Cleveland and elsewhere “where are the jobs?” in critiquing the president’s economic agenda.

“Well, after 12 million new jobs . . . I’ve come here not only to answer that question, but I want to return to the debate that is central to this country and the alternative economic theory presented by the other side,” Obama said.

The administration announced that the federal government is joining with the private sector to direct nearly $500 million toward manufacturing-focused initiatives, including a new, textiles-focused manufacturing institute competition led by the Department of Defense and a $320 million competition to help small manufacturers in 12 states.

To emphasis the initiative, Obama visited a manufacturing incubator in Cleveland that, among other things, houses a bourbon company that uses a scientific process to more quickly age its spirits.

“‘I’m not sampling any before the speech,” the president quipped to reporters, “but I may take a bottle home with me as a taste test.” When asked what Senate Majority Leader Mitch McConnell (R-Ky.) might think of it, Obama mused: “McConnell might have a different opinion about it. And I love Kentucky bourbon. But apparently this gets made a lot quicker.”

In an interview Tuesday, Sen. Sherrod Brown (D-Ohio), who rode with Obama to Cleveland on Air Force One, said the contrast between the two parties on the economy is clear.

“What we’re trying to do together on manufacturing will really matter for middle-class wages,” Brown said, noting that the federal government has already created a manufacturing hub in Youngstown and just opened a joint hub between Michigan and Ohio based in Detroit.

President Obama answers audience questions at the City Club of Cleveland. (Brendan Smialowski/AFP/Getty Images)

Speaking to reporters Tuesday, House Majority Whip Steve Scalise (R-La.) said voters can look at the resolution they crafted to get a sense of where the GOP would take the country if they controlled the executive as well as the legislative branch.

“Our budget is our vision for how to get the country back on track, how to address the big problems that Washington is facing,” he said. “And it stands in stark contrast to the vision that the president’s laid out, not only in his policy, but also in his budget.”

Americans are more optimistic now about the economy than they were before the November mid-term elections, in part because of lower gas prices and more robust job growth — two factors which have made politicians more eager to discuss the nation’s economic outlook.

The country has added 877,000 manufacturing jobs since February 2010, according to the White House, the fastest rate of manufacturing job growth since the 1980s.

But Republican pollster David Winston said that the Obama administration invariably turns to federal spending to spur economic growth, rather than reducing more of the barriers to private innovation. While Democrats have pushed for a mandatory increase in the minimum wage, Winston argued that fast-food workers in boom towns in North Dakota are earning higher wages because the demand for labor is so high there.

“He has put policies in place that helped government, but did not affect the private sector in a way that leads to increased wages,” Winston said.

But Democrats say increasing Americans’ educational and skills training represent a more certain path to climbing the economic ladder. The White House announced it will spend $158 million — matched by another $158 million in private funds — to provide technology and engineering expertise to small manufacturers over the next five years through the Manufacturing Extension Partnership, a state-federal network.

Brown said recent economic history underscores problems with GOP proposals to cut taxes as a way to spur economic growth.

“When you invest in the '90s, you get 22 million jobs. When you have tax cuts and trickle-down economics in the next decade, you get no job gain,” he said, adding that the United States has had uninterrupted growth over the past 60 months under Obama’s time in office. “If that’s not enough evidence, I don’t know how you convince people who just want to do trickle-down.”

Public perception of who is more capable of reviving the economy is critical in determining the outcome of elections. In both the 2012 and 2014 elections, the number of voters who said the economy’s condition was “not so good” comprised nearly half the electorate — 45 percent in 2012 and 48 percent two years later.

In 2012, Republicans lost those voters by 13 points, but in the 2014 election the GOP won them by 17 percent.

“Granted, it’s a different electorate,” said Winston, noting that off-year elections tend to bring out more conservative voters. But he added it still has implications for those vying for the White House in 2016. “One of the challenges to all of these Republican candidates is, who has the compelling economic idea that helps frame the Republican debate? I don’t think we’ve gotten to that point yet.”

Eilperin reported from Washington. Paul Kane contributed to this report.