Representative Eric Cantor of Virginia, the House majority leader, said earlier this year that he would try to prevent votes on measures that were not “substantive and meaningful.” The House did not vote, for example, on an independent resolution, passed in the Senate this year, to honor the troops who carried out the mission that killed Osama bin Laden. His office did not respond to a request for comment on Tuesday.

Five Democrats on the House Judiciary Committee wrote a dissent against the motto resolution last March, and Representative Jerrold Nadler of New York spoke against it Tuesday in a brief debate on the House floor.

“Why are my Republican friends returning to an irrelevant agenda?” Mr. Nadler said. “The national motto is not in danger. No one here is suggesting we get rid of it. It appears on our money, it appears in this chamber above your head, it appears in the Capitol Visitors’ Center, all over the place.”

The motto’s words have been the subject of discussion before. President Theodore Roosevelt wrote a letter in 1907 explaining the logic behind leaving “In God We Trust” off a $10 gold coin.

“To put such a motto on coins,” Roosevelt wrote, “or to use it in any kindred manner, not only does no good but does positive harm, and is in effect irreverence, which comes dangerously close to sacrilege.”