Leading Democrats inside and outside Congress have hit upon a strategy to curtail a recent epidemic of corporate tax dodging, which if left unchecked could cost the government tens of billions of dollars. It begins today with a closely watched hearing in the Senate Finance Committee, a prelude to a whirlwind of horse trading and demand-setting among policymakers.

As analyst David Cay Johnston observed, corporations like AbbVie, makers of Adderall, use a process known as inversion to merge with smaller companies located in tax havens like Ireland, Luxembourg or the Cayman Islands. Then, the domestic firm changes its corporate billing address to that of the overseas company, adopting their lower tax rate and reducing or eliminating their U.S. corporate tax burden.

AbbVie shares almost no business overlap with the small Irish company, Shire, with which it merged earlier in July. Shire’s CEO admitted last month, “I think the main strategic rationale here is tax inversion.” The new company will be re-incorporated on the island of Jersey, a notorious tax haven located in the English Channel. But its corporate headquarters will remain in America, along with its production, sales and research offices. The Jersey re-incorporation exists only on paper. “It will be domiciled in the UK for tax purposes,” said AbbVie’s chief executive, Richard Gonzalez, in announcing the deal.

These inversion deals have increased lately, with 14 announcements this year, from drug companies Mylan and Actavis to the medical device company Medtronic. According to an analysis by Goldman Sachs, completed and pending inversions in 2014 outpace all of those performed between 2002 and 2013.

This has caught the attention of lawmakers, especially because of the money at stake. The Joint Committee on Taxation estimates that inversions will cost the federal government $19.6 billion in tax revenue over the next 10 years. “As long as these inversions are legal, companies are going to do them,” said Rep. Keith Ellison, D-Minn., co-chair of the Congressional Progressive Caucus. “If they didn’t, their shareholders might even sue them.”

Currently, a foreign entity need only control 20 percent of the merged company for the billing address to shift overseas to the tax haven. The Obama Administration has proposed to increase that to 50 percent, in an effort to make the deals less attractive. Treasury Secretary Jack Lew wrote to House Republican leaders last week urging them to “shut down this abuse of our tax system.”

Republicans have said that they would rather deal with inversions in the context of overall tax reform, and with precious little time between now and the midterm elections, rapid action on the issue appears remote. However, activists working to stop inversions believe they have a wild card: the tax extenders bill, a large set of mostly corporate tax breaks typically passed on an annual basis.

The latest round of tax extenders expired at the end of 2013, and Congress has until the end of this year to enact them retroactively. The Senate Finance Committee advanced a bill earlier this year, but it stalled in the full Senate over an argument about amendments. Meanwhile, the House’s tax extender packages look very different from the Senate’s. Observers believe the matter will not get resolved until the lame duck session after the elections.