Against the backdrop of a presidential veto threat, the House readied a vote on an eavesdropping bill that would expand court oversight of government electronic surveillance in the United States.

The bill, which was scheduled for a vote Wednesday, allows unfettered surveillance of foreign targets but requires special authorization if the foreign targets are likely to be in contact with people inside the United States — an effort to safeguard Americans' privacy.

Critics of the bill say the authorization, commonly referred to as a "blanket warrant," will tie up intelligence agents in red tape, impeding them from conducting urgent surveillance of terrorist suspects.

The White House threatened again on Tuesday to veto the measure unless substantive changes are made.

President Bush's central objection is the bill's lack of retroactive immunity for telecommunications companies that allegedly violated wiretapping and intelligence laws by secretly providing the government access to Americans' e-mails and phone records without court orders.

House Majority Leader Rep. Steny Hoyer, D-Md., has said no immunity will be granted until the White House tells Congress exactly what the telecommunications companies did that requires legal protection. The top Republican on the Senate Judiciary Committee Sen. Arlen Specter, R-Pa., joined Tuesday with the Democrats, saying he would not support a retroactive immunity provision until Congress is informed what the companies did.

Telecommunications companies face roughly 40 lawsuits in U.S. civil courts for their alleged cooperation with government surveillance of Americans without the appropriate court orders. The Bush administration warns that without immunity, if the companies are found guilty they could be bankrupted by the penalties.

The Senate's version of the surveillance bill is expected to be unveiled on Thursday. The Senate bill is not finalized but is more likely to include an immunity provision, according to a person close to the process who demanded anonymity because the measure wasn't final.

The House would explicitly allow surveillance without a court order of illegal immigrants in the United States. It also lengthens the statute of limitations on violations of the electronic surveillance law from five years to 10 years, and it allows emergency electronic surveillance to continue during an appeal if a court order is denied.

The new bill would amend the 1978 Foreign Intelligence Surveillance Act, which dictates when the government must obtain eavesdropping warrants from a secret intelligence court.

That law was last changed in August, after the administration argued technological advances had made the old law too cumbersome and created a dire gap in its intelligence collection. The updated law allowed the government to eavesdrop without a court order on communications conducted by a person reasonably believed to be outside the U.S., even if an American is on one end of the conversation — so long as that American is not the intended focus or target of the surveillance.

Civil liberties advocates and Congress' Democratic leaders have argued the new law, which expires in January, doesn't adequately protect Americans' privacy.