Small government conservatives and liberal Democrats have backed the amendment, which dovetails with another to cut off funds for the NSA. Both measures drew criticism from the leaders of the Senate Intelligence Committee, who argued that the surveillance programs have helped disrupt numerous attempted terrorist attacks.
The House is likely to vote on the amendments Wednesday.
Snowden leaked documents last month that revealed that the NSA had collected phone records, while a second NSA program forced major Internet companies to turn over contents of communications to the government.
Leaders in Congress, such as House Speaker John Boehner and House Intelligence Committee Chairman Mike Rogers have strongly defended the programs, but libertarian lawmakers and liberals have expressed serious concerns about the government's surveillance in a fierce debate over privacy and national security.
The overall defense spending bill would provide the Pentagon with $512.5 billion for weapons, personnel, aircraft and ships plus $85.8 billion for the war in Afghanistan for the fiscal year beginning Oct. 1.
But the House version would still have to be reconciled with a version being drawn up in the Senate and any eventual bill could still be vetoed by President Barack Obama.
The bill is $5.1 billion below current spending and has drawn a veto threat from the White House, which argues that it would force the administration to cut education, health research and other domestic programs to boost spending for the Pentagon.
In a leap of faith, the bill assumes that Congress and the administration will resolve the automatic, across-the-board spending cuts that have forced the Pentagon to furlough workers and cut back on training. The bill projects spending in the next fiscal year at $28.1 billion above the so-called sequester level.
Republican leaders struggled to limit amendments on the overall bill, concerned about hampering the president's national security and anti-terrorism efforts.
At issue is where to draw the appropriate balance between national security in a post-9/11 America and the right to privacy that Americans expect to enjoy. National security hawks argue that the surveillance programs have helped disrupt numerous attempted terrorist attacks, and warn that future attacks will be harder to prevent if the programs are dismantled. But libertarians and others have contended that the programs constitute an overly broad intrusion into people's communications that, because they're kept secret, have little accountability.
The House also will consider an amendment that would bar funds for any military action in Syria if it violated the War Powers Resolution which requires that the president seek congressional approval for any act of war. Another amendment would prohibit money to fund military or paramilitary operations in Egypt.
Republicans and Democrats argued that Congress should have a say in what amounted to taking sides in a sectarian war.
The debate over Syria comes as the chairman of the Joint Chiefs of Staff, in a cautionary assessment of more aggressive American military action, said establishing a no-fly zone to protect Syrian rebels would require hundreds of U.S. aircraft at a cost of as much as $1 billion a month with no assurance it would change the momentum in the 2-year-old civil war.
In a letter to the chairman of the Senate Armed Services Committee, Gen. Martin Dempsey outlined the risks, costs and benefits of five potential steps as the Obama administration weighs its next move to help the opposition battling the forces of President Bashar Assad. The sectarian conflict has killed at least 93,000, according to United Nations estimates, and displaced millions, prompting more calls on Capitol Hill for greater American action.
Dempsey said the decision to use force in Syria is not one to be taken lightly.
Separately, members of the House Intelligence Committee who had balked weeks ago at the Obama administration's first attempt to pay for lethal aid for the Syrian rebels said Monday that their concerns largely had been addressed.
"After much discussion and review, we got a consensus that we could move forward with what the administration's plans and intentions are in Syria consistent with committee reservations," Rogers said in a statement.
Money to arm the rebels would come from current classified intelligence budgets.
At a Capitol Hill news conference on Tuesday, Boehner expressed his support for the move.
"I think their effort to help the right set of rebels in Syria is in our nation's best interest," he told reporters.