THE MARGIN by which the House of Representatives approved the Metro financing bill yesterday was stunning. Even the subway's most devoted friends did not expect the bill to pass so handily (261 to 125) after the Carter administration made a last-minute effort to kill it. But common sense and a feeling of responsibility toward a mass-transit system it has nurtured from the beginning prevailed, and the House gave Metro a boost it desperately needed.

The bill provides an additional $1.7 billion over six years in federal matching funds. It is the second part of a three-piece financing package put together in laborious negotiations by Metro, the local governments, the Department of Transportation and congressional leaders. The first part was the release last week by Secretary of Transportation Brock Adams of a billion dollars in interstate highway funds originally earmarked for roads that now will not be built.

If the Senate concurs in the judgment the House had made, the success of this financing package (and completion of the full 101-mile system) will rest squarely on the local governments and the states of Maryland and Virginia. Their share - the third part - is $400 million to match the funds of the House has authorized.

The opposition of the Carter administration to this arrangement, which came to light only yesterday morning, must have come from the anti-Washington strain in President Carter's Sunday night speech, not his pro-mass-transit strain. Otherwise, it is inconceivable that the administration could have opposed this bill. Metro is the one new mass-transit system in the nation that is on the verge of having a substantial impact on commuter and, thus, gasoline-consumption habits.