The vote on Wednesday comesof programs that collect the phone logs of millions of Americans as well as internet data from the accounts of foreign targets.
A handful of liberal Democrats have joined Tea Party conservatives in the House of Representatives in sponsoring an amendment to halt NSA surveillance of Americans who are not connected to an ongoing probe.
Republican congressman Justin Amash tweeted his thanks to House Speaker John Boehner for bringing the amendment — which is tacked on to the defence spending bill under review — up for open debate this week.
The bill also requires that secret Foreign Intelligence Surveillance Act (FISA) court opinions be made available to congress and that summaries of those opinions be made public.
House Democrats John Conyers and Jared Polis joined Amash's amendment, which they said "makes sure that innocent Americans' information isn't needlessly swept up into a government database".
Even if the amendment passes the House it would face an uncertain fate in the Senate, although top Senate Democrat Harry Reid suggested he would be open to considering the legislation.
"We need as much transparency as possible," Reid said Tuesday.
But Democrat Dianne Feinstein, chair of the powerful Senate intelligence committee, and the panel's ranking Republican Saxby Chambliss, issued a curt warning about the amendment, saying the programs are needed to foil terror attacks.
They assured lawmakers that the data-mining program is under "strict controls" and has been authorised by all three branches of government.
The White House also came out against the amendment on Tuesday, saying it would "hastily dismantle one of our intelligence community's counterterrorism tools.
"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."