Some of the lawmakers said their vow to forgo pay was good only for as long as the shutdown lasted. When the shutdown ended after 16 days, they said, they had done their jobs and were entitled to their money.

Others among the nearly 250 who forsook their salaries said congressional approval of back pay for all federal workers, including the hundreds of thousands who were furloughed, meant lawmakers should be paid, too.

David Williams, president of the Taxpayers Protection Alliance, said members of Congress are using technicalities to try to “wiggle out” of promises to the American people.

“People across the country, when they heard their member of Congress said they would be returning their pay during shutdown, that’s what they heard and what they expected,” Mr. Williams said. “For Congress to even try to backtrack on that just reduces the amount of trust people have in Congress, if that’s even possible.”