Republicans and Democrats don’t see eye-to-eye on most economic issues, but those with a keen ear on Monday may have heard an unusual instance of leaders of both parties echoing each other’s rhetoric.

House Majority Leader Eric Cantor (R-Va.), who was giving a speech at Stanford University’s Hoover Institution billed as an unveiling of House Republicans’ “pro-growth economic plan,” pushed for the need to encourage American innovation – a point frequently emphasized by congressional Democrats and the White House.

“Americans will out-work, out-hustle and, yes, out-innovate the rest of the world,” Cantor said. (Senate Democrats last month held a press conference in which they, too, called for America to “out-innovate” its competitors.)

But the similarities didn’t stop there. Cantor went on to talk about “winning the future” – employing a signature phrase from President Obama’s State of the Union address earlier this year.

“Winning the future will only be hard if we lose out to the bureaucrats, technocrats and would-be autocrats punishing our progress,” Cantor said. “Fifty years from now, people will look at 2011 as the year we began our comeback or the year that we continued our fallback. Let us resolve to work together to make sure that the future belongs to us.”

New York Democratic Sen. Charles Schumer, meanwhile, issued a pre-buttal of Cantor’s speech in which he slammed Republicans on jobs but interestingly touched on the matter of federal regulation – an issue House Republicans have focused on as part of their “cut-and-grow” agenda.

“Since taking over the House, Republicans have been too busy jamming a far-right social agenda onto the federal budget to bring up a single jobs bill for a vote in the House,” Schumer said in a statement. “They have voted to raise taxes on small businesses and end loan guarantees that provide important access to capital. Each day, House Republicans are proving that too much ideology in government is a burden for U.S. businesses just like too much regulation is.”

As he has previously, Cantor on Monday emphasized the need to promote the success of the private sector by cutting spending and regulation, particularly with regard to so-called “gazelles,” or innovation-based start-ups. He also announced that Republicans will bring to the floor a bill that would reduce the corporate tax rate to 25 percent from its current level of 35 percent, a plan House Ways and Means Committee Chairman Dave Camp (R-Mich.) previewed last week in an interview with the Wall Street Journal.

Democrats, meanwhile, have argued that government must invest in industry and education in order to promote innovation; they have also highlighted the benefits of regulation and noted that government rules are necessary to protect the public.

Those facts serve as a reminder that, when it comes to achieving the goal of innovation, just as on the issue of job-creation, both parties have markedly different ideas on how to progress – even if their rhetoric occasionally does overlap.

Asked Monday about the choice of “winning the future,” Cantor’s deputy chief of staff, John Murray responded, “Does Obama own that? I don’t think so.”

“Anyway, the president’s rhetoric doesn’t match up with his policies — period,” Murray continued. “Eric believes spending cuts combined with helping lower barriers for America’s innovation-based start-ups — those gazelles — is the central prescription for getting our economy back on track and grow it over the long-term. We’ve got tough choices to make if we’re going to preserve people’s fair shot at earned success.”

Meanwhile, it’s worth noting that the idea that government over-regulation can be a burden on business is not an exclusively Republican idea, either; Obama himself called for a review of existing federal regulations earlier this year.