The programme, which permits surveillance of communications between people in the US and others overseas if one has suspected ties to terror suspects, was authorised by Bush shortly after the September 11 attacks in 2001.
"Some people around here get cold feet when threatened by the administration"
Patrick J Leahy, senator for Vermont
On Wednesday, some Democrats criticised party members in the senate who they said had voted in favour of the bill out of fear of appearing soft on security issues.
"Some people around here get cold feet when threatened by the administration," Patrick J Leahy, senator for the US state of Vermont, was quoted by the New York Times as saying.
The bill, if made law, would also grant retroactive immunity to telephone companies that took part in the programme.
About 40 civil lawsuits have also been filed against several US phone companies which are accused of violating US citizens' rights to privacy.
However, Bush said it was vital that the companies be shielded from such lawsuits, otherwise "they won't help to protect America".