The House approved the measure on Wednesday by 251 votes to 174. Supporters said that it would balance civil liberties with the need to bolster national security.
But a number of Democrats and Republicans vowed to oppose the legislation in the Senate.
They said that despite increased congressional and judicial oversight, it would still give the government too much power to pry into the lives of Americans, including their medical, gun and library records.
Opponents have threatened a Senate procedural roadblock known as a filibuster.
It was unclear if they could prevent backers from mustering the needed 60 votes in the 100-member, Republican-led chamber to prevent such a tactic.
A vote was set for Friday.
A Senate Democratic leadership aide said opponents seemed to have from 40 to 46 votes to sustain a filibuster.
Republicans said it was uncertain how many votes they would have. "It's going to be close," a Senate Republican aide said.
"I urge the Senate to pass this legislation promptly and reauthorise the Patriot Act"
Bush weighed into the fray, saying in a statement: "The Patriot Act is scheduled to expire at the end of the month, but the terrorist threat will not expire on that schedule.
"In the war on terror, we cannot afford to be without this law for a single moment. I urge the Senate to pass this legislation promptly and reauthorise the Patriot Act."
The Patriot Act was first passed after the 11 September 2001 attacks on the US to expand the power of the federal government to track down terrorists.
The House-passed compromise would make permanent 14
provisions set to expire on 31 December, including ones allowing the sharing of information by intelligence and law-enforcement agencies.
In a concession to critics, the legislation would extend three others by four years, rather than seven years as proposed earlier.
Those provisions cover rules for tracking "lone-wolf" terrorists, who operate independently of known groups, as well as wiretaps and court orders for records from businesses, libraries and others in intelligence cases.
The legislation would amend the ability of law-enforcement
agents to obtain library records, requiring a court to be
satisfied that the records were relevant to a terrorism investigation.