Under the bipartisan bill, which passed, the Patriot Act would be changed to prohibit bulk collection by the National Security Agency of metadata charting telephone calls made by Americans. In addition, the legislation would bar permitting bulk collection of records using other tools like so-called national security letters, which are a kind of administrative subpoena.

The near unanimity in the House is not reflected in the Senate, where a bipartisan group that backs the House bill faces opposition from Mr. McConnell and a small but powerful group of defense hawks who want no change, and from another faction led by Senator Rand Paul, Republican of Kentucky, that is pressing for even greater restrictions of data collection.

A compromise of some form must be reached before June 1, when the provision of the Patriot Act that allows the N.S.A. dragnet expires.

“I think we have found an equilibrium on how to protect both security and privacy,” said Representative Adam B. Schiff of California, the ranking Democrat on the House Intelligence Committee.