The White House is urging Congress to reject an attempt to stop the NSA collecting Americans’ phone records.
With a key vote coming up, President Barack Obama’s spokesman said curbs on the NSA would “hastily dismantle” a vital counter-terrorism tool.
NSA chief General Keith Alexander spent Tuesday lobbying Congressmen to vote against the proposed measure.
Critics say NSA phone data collection is an unwarranted invasion of privacy.
The details of the programme were made public by Edward Snowden, who had worked for the NSA and is now a fugitive, awaiting a decision on his asylum application in Moscow.
House of Representatives Republican Congressman Justin Amash has introduced an amendment to a defense spending bill, which would block funding for the NSA’s programme to collect details of every call made by or to a US phone.
Justin Amash said: “My amendment blocks funding of NSA’s collection of personal data if that data does not pertain to a person under investigation.”
A vote on the amendment will take place on Wednesday.
Even if it passes the House, the measure is seen as unlikely to become law, as Barack Obama’s Democratic Party controls the Senate.
House Democrats John Conyers and Jared Polis supported the move, which they said “makes sure that innocent Americans’ information isn’t needlessly swept up into a government database”.
However, the White House said the measure would deprive the intelligence agencies of a key tool in preventing terror attacks.
“This blunt approach is not the product of an informed, open or deliberative process,” said spokesman Jay Carney.
“We urge the House to reject the Amash amendment, and instead move forward with an approach that appropriately takes into account the need for a reasoned review of what tools can best secure the nation.”
NSA head Gen. Keith Alexander held separate, closed-door sessions with Republicans and Democrats on the eve of the vote in an attempt to persuade them to vote against.
Afterwards he told CNN: “What you can see is that everybody wants to ensure we protect civil liberties and privacy and defend this country.
“We have that responsibility, and the issue is, how do we do that? How do we take care of our people and protect our civil liberties and privacy? This is a tough issue.”
The issue has split the main parties, with Democrats and Republicans lining up on both sides of the debate.
Meanwhile it is thought possible that Russia will announce whether Edward Snowden has been successful in his application for temporary asylum in the country.
Edward Snowden has been in limbo in a Moscow airport for weeks, but his lawyer Anatoly Kucherena says Wednesday is the deadline for the Federal Migration Service to rule on his request.
A number of Latin American states say they are willing to offer the former intelligence systems analyst asylum, but the lawyer says Edward Snowden first needs Russian asylum in order to be able to travel, since the US has cancelled his passport.
The US has charged Edward Snowden with leaking classified information.
President Vladimir Putin has refused to hand him to US authorities, but says he can only stay in Russia if he stops leaking secrets about US surveillance schemes.