Senate Homeland Security and Governmental Affairs Chairman Joe Lieberman (ID-Conn.) is pushing ahead with legislation stripping “citizenship rights” of Americans associated with terrorist organizations.

Lieberman, along with co-sponsor Sen. Scott Brown (R-Mass.) and Reps. Jason Altmire (D-Pa.) and Charlie Dent (R-Pa.), will introduce the Terrorism Expatriation Act on Thursday.

Although Senate Democratic Conference Vice Chairman Charles Schumer (N.Y.) on Tuesday indicated he might end up backing the bill, Schumer spokesman Brian Fallon on Wednesday closed the door on the possibility, saying Schumer views the proposal as ineffective and unconstitutional.

“Having learned about the proposal, the Senator believes it would be found unconstitutional and would also be ineffective in this context. There are much better ways of obtaining information from terrorists,” Fallon said.

Although details of the bill remain unclear, in a statement Lieberman’s office described the bill as “bringing existing federal law up to date by adding another item to the list of acts for which a U.S. national would lose his/her nationality: providing material support or resources to a Foreign Terrorist Organization, as designated by the Secretary of State, or actively engaging in hostilities against the United States or its allies.”

However, the law would only apply in situations in which an American citizen was involved with a foreign terrorist organization and whom the State Department has determined was intending to renounce his citizenship.

Requiring a citizenship renunciation finding would likely mean that Irish-Americans and others with ties to quasi-terrorist organizations such as the Real IRA would not be covered by the law.

However, the requirement could rule out someone like Faisal Shahzad — whose alleged attempted Times Square bombing was the impetus for Lieberman’s bill — because it remains unclear if he took any steps to renounce his citizenship.