President Obama spent Monday huddling with Ireland’s president and prime minister in Dublin, visiting a village where his great-great-great grandfather lived and drinking a pint of Guinness, among other activities.

He did not, news reports suggest, engage anyone in an argument about the definition of an earmark. But back home, that debate rages on.

In March, Obama signed a short-term spending resolution that included a handful of specific cuts, including one slashing $17 million for the International Fund for Ireland, a group that promotes peace and reconciliation between nationalists and unionists in the Emerald Isle. The cut marked a rare example of agreement between House Republicans, many of whom consider the program a poor use of U.S. money, and the White House, which zeroed out funding for the IFI in its 2011 budget request.

But some government programs, like horror-movie villains, are stubbornly unwilling to die, even after they’ve gotten the ax, and now Rep. Peter T. King (R-N.Y.) is leading a group of lawmakers hoping to restore money for the IFI. That effort has renewed debate not just about the merits of the donation, but also whether it constitutes an earmark — or perhaps an Éiremark? — and thus should be prohibited under the House GOP’s rules.

In a “Dear Colleague” letter circulated to House members last week, King and Rep. Joseph Crowley (D-N.Y.) asked the House Appropriations Committee to give the IFI $17 million in 2012. The letter got 19 signatures.

“Now is the time for the United States to stand in solidarity and continue supporting Northern Ireland,” they wrote, adding: “With 35 million Americans of Irish descent, our ties to Ireland are strong, and our interests are well-served by remaining deeply engaged in the peace process.”

King said that Irish and British government officials strongly encouraged him to pursue the funding. “I’m supporting it as much for diplomatic reasons as any,” he said.

One of the first things Republicans did after taking over the House majority was to adopt a ban on earmarks. So does King’s letter — requesting a specific amount of money for a specific group — violate that ban?

“We’re definitely in a very gray area,” said Steve Ellis, vice president of the watchdog group Taxpayers for Common Sense.

House rules define an earmark as “a provision or report language included primarily at the request of a Member . . . providing, authorizing or recommending a specific amount of discretionary budget authority, credit authority, or other spending authority for a contract, loan, loan guarantee, grant, loan authority, or other expenditure with or to an entity, or targeted to a specific State, locality or Congressional district, other than through a statutory or administrative formula driven or competitive award process.”

At the most basic level, King’s effort on behalf of the IFI involves a member “recommending” money for “an entity,” but of course it’s not that simple.

The Appropriations Committee doesn’t consider the IFI funding an earmark under House rules, according to a panel aide. Under the new anti-earmark regime, the committee has been on the lookout for spending items that benefit specific companies or geographical locations, especially within members’ districts. King may have been considered for U.S. ambassador to Ireland but he does not, in fact, represent Ireland.

Ellis, whose group has not branded IFI money as an earmark in the past, made a similar point.

“Normally when you think about earmarks you think about it going to your home district — bringing home the bacon,” he said. “This is not the same thing in that respect.”

But not all watchdog groups think alike.

Citizens Against Government Waste does consider cash for the IFI an earmark. Since 1986, the group noted on its Web site in April, the IFI has received nearly $500 million from the U.S. government. “This figure includes $281 million in earmarks identified by [CAGW] since 1995,” the group wrote.

For some earmark-watchers — a small but proud Washington breed — a dividing line exists between the projects that are requested in the president’s budget and those that aren’t. Obama didn’t ask for the IFI funding in his 2011 budget but he did for 2012 (although his submission appears to ask for less than $6 million).

Then there’s the question of whether the IFI even wants the money. In its annual report for 2009, the group said it would not seek any more international contributions after 2010 (it has also received donations from the European Union, Canada, Australia and New Zealand). But the Irish economy’s free-fall prompted the IFI to reverse course, and now it does want the cash.

Rep. Jason Chaffetz (R-Utah), who sponsored a stand-alone bill this year to kill the U.S. contribution to the IFI, acknowledged last week that he “wouldn’t necessarily consider that money an earmark.” He calls it something else: wasteful.

“If we can’t kill this, we can’t kill anything,” Chaffetz said. “I can’t believe somebody’s trying to bring this back.”