Companies that bring jobs from overseas back to the United States would get some economic rewards for doing so, under a new bill unveiled by Sen. Mark Warner (D-Va.) and Rep. Frank Wolf (R-Va.) on Friday.

The two Virginians are promoting their effort as a relatively rare bipartisan, bicameral initiative to boost job creation at a time when unemployment remains stubbornly high and polls show broad national pessimism about the economy. The measure incorporates elements of separate bills they had introduced previously.

“Both of us have a passion about this,” Warner said on a conference call with the media, dubbing their partnership an effort to move something substantive at a time when “not a lot is getting done” on Capitol Hill.

Under their plan — dubbed the America Recruits Act of 2011 — companies could get a forgivable loan for as much as $5,000 for each new manufacturing job they create in the United States. Up to $1,000 of the loan would be forgiven each year, giving companies an incentive to maintain the job for at least five years rather than taking the government money and running.

Their bill would also help companies develop better training and education programs and make federal financial help more easily available to companies exporting products from the United States.

Warner said the cost of the bill would be “roughly in the $100 million range,” but both lawmakers stressed that the measure did not involve new federal spending. Rather, the plan would reallocate existing funds already in the U.S. Commerce Department budget.

“We’re changing the eligibility of some of these current grants,” Wolf said.

Wolf is chairman of the House Appropriations subcommittee that includes the Commerce Department budget, and he said he plans to put their new legislation in the spending bill that his subcommittee passes in the coming weeks. It’s not clear how or when the measure might move in the Senate.

As an example of the kind of projects that might be aided by their bill, Warner cited CGI Group Inc.’s decision five years ago to locate new technology jobs in southwest Virginia. Wolf noted that the wireless firm Simplexity had chosen to locate a call center in Reston rather than overseas.