WASHINGTON (Reuters) - Pfizer Inc (>> Pfizer Inc.) faces political risks in Washington if it proceeds with a bid for Allergan (>> Allergan, Inc.), but with little chance of legislation to curb such tax inversion deals, the Obama administration may be able to throw up only limited obstacles.

Lawmakers are widely seen as unlikely to tackle major tax code changes before the 2016 presidential election, but they were already scolding Pfizer publicly on Thursday, showing that companies considering inversion deals do face reputational risk.

"When corporations choose to invert and don’t pay their fair share of taxes, they leave the rest of us to pick up the tab. That isn't right," said Democratic Senator Richard Durbin in a statement. Durbin has voiced similar views on prior inversions, including one that was abandoned by retailer Walgreen (>> Walgreens Boots Alliance Inc).

An inversion deal typically involves a U.S. company buying a foreign company and then relocating corporate headquarters, on paper at least, to the foreign company's home country, with the goal of reducing the combined company's overall taxes.

New York-based Pfizer and Dublin-based Allergan said they have not reached an agreement and declined to give details.

A tax inversion is being discussed in the current talks, which could create the world's largest drugmaker, a person familiar with the matter told Reuters.

Ireland has been a frequent redomiciling destination for U.S. corporations fleeing the U.S. tax system, though most of them leave their actual core operations in the United States.

The latest wave of inversions crested in late 2014, when the Obama administration cracked down, making it harder both to do the deals and to realise their benefits.

A U.S. Treasury Department spokesperson said further actions could be taken, but stressed that only Congress can slam the door completely.

Among the department's options is tightening rules against a tax-dodging technique known as "earnings stripping" that is often a key component of inversions. This practise involves shifting profits earned in the United States to a lower-tax jurisdiction.

"We are continuing our review of a broad range of options for further action but there is a limit to what we can do administratively. Congress must take action to end this loophole‎," the Treasury spokesperson said in a statement.

Steven Rosenthal, senior fellow at the Urban-Brookings Tax Policy Centre, a think tank, agreed that earnings stripping was a good place for the Treasury to start.

"Otherwise you leave a loophole and incentive for these combinations to continue," he said.

(Reporting by David Lawder; Editing by Kevin Drawbaugh and Christian Plumb)

By David Lawder