Rogers joined six GOP chairmen in a letter urging lawmakers to reject the Amash amendment.
"While many members have legitimate questions about the NSA metadata program, including whether there are sufficient protections for Americans' civil liberties," the chairman wrote, "eliminating this program altogether without careful deliberation would not reflect our duty, under Article I of the Constitution, to provide for the common defense."
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 next budget year.
The total, which is $5.1 billion below current spending, 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 in order 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 led 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.
By voice vote, the House backed an amendment that would require the president to seek congressional approval before sending U.S. military forces into the 2-year-old civil war in Syria.
Rep. Trey Radel, R-Fla., sponsor of the measure, said Obama has a "cloudy foreign policy" and noted the nation's war weariness after more than 10 years of conflict in Iraq and Afghanistan.
The administration is moving ahead with sending weapons to vetted rebels, but Obama and members of Congress have rejected the notion of U.S. ground forces.
The House also adopted, by voice vote, an amendment barring funds for military or paramilitary operations in Egypt. Several lawmakers, including Rep. Kay Granger, R-Texas, who heads the panel overseeing foreign aid, expressed concerns about the measure jeopardizing the United States' longstanding relationship with the Egyptian military.
The sponsor of the measure, Rep. Thomas Massie, R-Ky., insisted that his amendment would not affect that relationship.
The overall bill must be reconciled with whatever measure the Democratic-controlled Senate produces.