FORTUNE — The multinationals pushing Washington to grant them a tax holiday on their overseas profits have had a lot to cheer about recently.

The notion appeared stillborn when the companies started trying to sell it earlier this year. Proponents argue it will provide a boost to the economy, but during a repatriation holiday in 2004, several of the biggest beneficiaries actually cut jobs after taking advantage of the break. And they directed most of the loot they brought home to stock buybacks and dividend payments, leaving their Congressional sponsors feeling burned.

But the idea has attracted a surprising amount of interest on Capitol Hill this fall. With the deficit-cutting fever inside the Beltway starting to break as the pressure mounts to address joblessness, and a big-money lobbying campaign promoting repatriation as the best fix on hand, an unlikely array of Members of Congress have embraced the idea in one form or another.

A pair of heavy-hitting Congressional leaders from opposite parties and opposite chambers — House Majority Leader Eric Cantor (R-Va.) and Sen. Chuck Schumer (D-N.Y.), the No. 3 ranking Democrat in the Senate — is giving it the hard sell. Earlier this month, the centrist Blue Dog Democrats in the House endorsed a version that would allow companies to bring earnings back to the U.S. at a bargain-basement 5.25% rate and with essentially no strings attached. And last week, a half-dozen House Republican freshmen hosted a conference call to tout their support.

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On the other side of the Capitol, Sen. Kay Hagan (D-N.C.) joined with John McCain (R-Ariz.) to pen a version that would set a top rate of 8.75% for repatriated earnings, though companies could earn a lower rate by hiring more workers. Schumer, meanwhile, has teamed up with Sen. Mark Kirk (R-Ill.), a moderate freshman, and is shopping an approach that would marry a repatriation holiday to an infrastructure program by dedicating the tax receipts to funding a bank for new projects.

With all of that in motion, it would seem the only questions remaining are what form the break will take and when it will come. Indeed, repatriation’s champions, both on the Hill and on K Street, have been trying to create a sense of inevitability to encourage lawmakers still wary of the political peril of backing a measure that looks like a corporatist giveaway. At the same time, the companies shilling for a holiday — a roster that includes Apple (AAPL), Cisco (CSCO), Duke Energy (DUK), Microsoft (MSFT), Oracle (ORCL), and Pfizer (PFE) — are hoping to stir a sense of urgency by making the case they’ll need to start investing the estimated $1.4 trillion they’ve got parked overseas if they can’t secure the break soon.

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But while the boosters have generated plenty of light for their cause, actual heat has been harder to come by. Despite the work by Schumer and Cantor, the top leaders in either chamber — Senate Majority Leader Harry Reid (D-Nev.) and House Speaker John Boehner (R-Ohio) — have remained mostly mum. The men who wield the gavels of the tax-writing committees aren’t huge fans of a holiday either. Senate Finance Chairman Max Baucus (D-Mont.) has been an outspoken critic of the 2004 tax break.

In the House, Ways and Means Chairman Dave Camp (R-Mich.) on Tuesday released a draft proposal for moving the U.S. to a territorial tax system that includes a form of repatriation: as part of the transition to the new regime, companies would pay a 5.25% rate on their foreign earnings, whether or not they brought those profits home over an eight-year window. And while Camp told reporters he didn’t view the proposal as working “at cross-purposes” with the holiday the multinationals are pitching, he is pursuing it in the context of a comprehensive overhaul of the code — a project the companies expect to take years, while they hope to secure their break within months.

That the effort has made it this far stuns some on the Hill. “These lobbyists have really gotten their hooks into these Members,” one senior Republican aide says. But the lobbyists themselves quietly acknowledge they’ve still got their work cut out. Schumer’s plan is widely expected to include prevailing-wage protections for new infrastructure projects that would make it a non-starter with the GOP. Linking repatriation to infrastructure was meant to attract support from labor — Andy Stern, former president of the Service Employees International Union, has been talking it up for a year — but the big unions view the tax holiday as so unsavory, they aren’t willing to hold their noses.

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“We view it as a continuation of a policy that encourages employers to move jobs overseas,” one top labor official says. There is no actual bill yet, but the AFL-CIO, AFSCME, and the SEIU itself are all likely to oppose it once there is.

The version offered by Hagan and McCain isn’t faring much better. One lobbyist working the issue says the companies have struggled to convince other Senators to sign on. Including the authors, the measure now counts ten cosponsors, but none of them is on the tax-writing Finance Committee.

Many undeclared lawmakers are waiting to see how the politics around the issue shape up. Meanwhile, some vocal detractors on the Hill are trying to make sure it doesn’t gain any more traction. Sen. Carl Levin (D-Mich.), Chairman of the Senate Permanent Subcommittee on Investigations, earlier this month issued a report blasting the companies that took advantage of the 2004 tax break for their job-creating performance in its wake and warning against reprising the idea. He could soon follow up with hearings.

And if repatriation’s boosters can somehow clear the Congressional hurdles, they’ve still got to win over an economic team at the White House that is by all accounts hostile to the idea.

One of the more optimistic scenarios supporters lay out has the Congressional super committee on debt reduction punting on tax reform when it issues its report next month. Then, sometime early next year, the imperative of providing a short-term economic jolt would compel a bipartisan compromise on a pared-down jobs bill that could join a repatriation holiday to Democratic priorities like extending the payroll tax cut and unemployment insurance.

But given that macro political factors are likely to shape the fate of the tax holiday, it’s worth considering the bigger picture. On the right, all of the momentum on tax reform is moving away from the kind of tinkering that a holiday on foreign profits would represent and toward something bold and sweeping — witness the jockeying among the Republican presidential hopefuls to offer plans that scrap the entire code and replace it with a flat tax.

On the left, the rise of the Occupy Wall Street movement is focusing long-simmering frustration in the Democratic base toward the party establishment’s hesitation to take on entrenched corporate interests. Against that backdrop, elected Democrats sign on to a major tax break for the biggest companies at their own peril.