Lawmakers are growing tired of corporate America's persistent efforts to dodge U.S. taxes.

In the past month, Congress and the White House have denounced a loophole that lets companies lower their tax rate by moving their headquarters overseas. These so-called "inversions" have been the subject on Congressional hearings and legislation to eliminate the tax benefit.

Now, a group of Democrats in Congress want to make sure that any company that incorporates overseas would be barred from doing business with the government.

The No Federal Contracts for Corporate Deserters Act (yes, that's really the name), would bar contracts from going to companies that reincorporate, are at least 50 percent owned by American shareholders and have no substantial business in the foreign country where they are incorporated.

We ought to put a stop to all inversions, but at the very least, we should stop these companies from receiving federal funding from the same American families who have to pick up the tax burden inverted companies shrug off,” said Sen. Carl Levin (D-Mich.), who introduced the bill in the Senate with Sen. Richard Durbin (D-Ill.). Reps. Rosa DeLauro (D-Conn.) and  Lloyd Doggett (D-Tex.) introduced a companion bill in the House.

This is not the first time that Congress has tried to prevent companies that use inversions from doing business with the government. Congress has passed several laws in the last dozen years to address the problem. But companies have been able to avoid the ban by exploiting a key loophole that exempts firms who have merged with or bought a foreign competitor.

It is the same sort of loophole that has allowed companies to circumvent a broader 2004 law that reduced the tax benefits of companies that incorporate overseas.

recent report from the Congressional Research Service found that 47 U.S. companies have reincorporated overseas since 2003, nearly double the amount that did in the 20 years before. At least a dozen of the companies that have inverted in the past four years --  including Stratasys and Alkermes --  have won government contracts during that time.

"The federal government has been subsidizing this bad behavior by continuing to reward inverted companies with lucrative federal contracts," DeLauro said. "These companies take advantage of our education system, our research and development incentives, our skilled workforce and our infrastructure, all supported by U.S. taxpayers, to build their businesses. But when the tax bill comes due, they hide overseas."

The widespread use of inversions gained attention in recent months when high-profile U.S. pharmaceutical companies -- Pfizer, AbbVie and Medtronic -- made bids to merge with overseas rivals. Critics of the deals viewed them as thinly-veiled attempts by American firms to shift their tax burden to countries with lower tax rates.

Treasury Secretary Jack Lew has urged Congress to take action to eliminate the tax benefits for companies that incorporate overseas, throwing his support behind retroactive legislation that would apply to many cross-border deals announced in the last year.

If the series of deals in progress go through, researchers at the Joint Commission on Taxation say they could rob the U.S. Treasury of $20 billion in revenue over a decade.

In his weekly radio address Saturday, President Obama called out corporations using inversions to skirt U.S. taxes.

"When some companies cherrypick their taxes, it damages the country’s finances," he said. "It adds to the deficit.  It makes it harder to invest in the things that will keep America strong, and it sticks you with the tab for what they stash offshore."

Obama said the best way to address tax avoidance is through comprehensive tax reform that lowers the corporate tax rate and simplifies the tax code. With little to no movement on that front, Obama urged lawmakers to at least close the inversion loophole.