It sounds like the perfect political gesture for the moment. Congress is getting ready for an epic fight over the national debt, and House rules allow members to give back a portion of their salaries for debt reduction.

Two of them do.

Sometimes, up to three.

Last fall — as the issue of spending helped Republicans storm back to power in the House — exactly one sitting Republican and one Democrat chose to dock their pay for the cause.

Together, they donated $2,610.39 that quarter.

That’s how much the debt grows every five one-hundredths of a second. The government burned through their gift in three beats of a hummingbird’s wing.

The story of this little-used payback program says something about the fight Congress is beginning. The debt is so huge, and the fight so joyless, that even congressmen — the masters of the empty but attractive gesture — appear to see little use in this one.

“Even if all members of Congress returned their full salaries in order to pay off the debt,” it would barely make a dent, Rep. Henry Cuellar (Tex.) said in an e-mail.

Cuellar is a “Blue Dog,” or more conservative, Democrat, and he has embraced the debt as a political issue. He has called for a balanced budget and for rooting out ineffective federal programs.

He does not give any of his salary back. “We need real solutions, not gimmicks,” Cuellar wrote.

This week, House and Senate leaders are headed for their latest regularly scheduled showdown over federal spending. House Republicans have called for billions in budget cuts: Now, they must work out a deal with Senate Democrats or risk a government shutdown after April 8.

Even if the two parties agree, new problems are waiting just offstage. There is next year’s budget, in which Republicans will propose more cuts. And there will be a battle over raising the nation’s legal debt limit.

In each case, the underlying worry is the national debt, which stands at $14.2 trillion. Over the past year, it has increased by an average of $48,940 every second, accelerated by accruing interest and new borrowing.

Last year, records show, only two House members donated a “Gift to the United States for Reduction of Public Debt” in every fiscal quarter. Each time, Rep. Spencer Bachus (R-Ala.) gave $414.39, and Rep. Tim Walz (D-Minn.) gave $2,196.

These two are a bit of an odd couple. Bachus, a former sawmill owner in Congress since 1993, is against the health-care reform law and for a constitutional amendment prohibiting same-sex marriage. Walz, a former teacher in office since 2007, takes the opposite position on both issues. The American Conservative Union gives Bachus a rating of 96, and Walz a 4.

But both are giving back previous congressional pay raises, trying to show solidarity with constituents suffering in hard economic times.

Bachus’s gift includes the cost-of-living raise he would have received in 2009. Walz is returning all the salary increases he has received since joining the House in 2006.

“That old adage [is] ‘It’s better to try and live a sermon than give one,’ ” Walz said in a telephone interview. He said he “just decided it was the right thing to do.”

The only other congressman to donate toward the debt in 2010 was Rep. Frank A. LoBiondo (R-N.J.). He gave $4,782 in the first quarter and nothing thereafter. His staff said the donation was a personal matter and declined to talk about it further.

The year’s donations from the House totaled $15,233.56. They were given to the federal Bureau of the Public Debt. There, the money was lumped together with gifts from the public: bequests from the dead, pennies from schoolchildren, checks from all over.

Despite the gift’s name, the money actually doesn’t go to pay back the nation’s creditors.

Instead, it is given to the General Fund, which pays for whatever new things the government wants to buy. The logic is that this lowers the debt, indirectly, by reducing what has to be borrowed anew.

“Very incrementally, it does,” said McKayla Braden, a spokeswoman for the debt bureau. “In tiny, tiny amounts.”

Last year, Americans — elected and unelected — gave $2.8 million. That kept the debt from growing . . . for 57 seconds.

Congressional records show the House program, around since at least the 1970s, has never drawn more than a fraction of lawmakers. (The Senate has no similar program.) But in the past, donations were far bigger. In 1994, for instance, more than a dozen lawmakers combined to donate $128,000.

In the past decade, participation has withered. Rep. Peter A. DeFazio (D-Ore.) used to give more than $1,000 a year; now that money goes to community-college scholarships in his district. Rep. Dan Burton (R-Ind.) stopped donating after a $257 gift in 2009. His staff did to respond to requests asking why.

And the program (which House officials do little to publicize) has drawn in few new donors, even among the loudest advocates for shrinking the debt.

“Where I can have a bigger effect is on my own personal budget” for office expenses and staff salary, said Rep. Jason Chaffetz (R-Utah), a prominent voice for cutting spending. Rep. Ron Paul (R-Tex.), one of the right’s most famous worriers about the debt, also makes a point of returning unused office funds.

At the Republican Study Committee — a group of 175 House members, and a loud voice for cutting spending — spokesman Brian Straessle said this was not a mistake. He said that giving money toward the debt wouldn’t solve anything: What the government needs is to learn to live with less.

“Uncle Sam doesn’t need a bigger chunk of your paycheck,” Straessle said. Of his group, Bachus was the only member to donate last year. “He needs to kick the spending addiction.”

And there was agreement from one of the most important groups egging these congressmen to take on the debt issue. “We’re looking for substance above symbolism,” said Mark Meckler of the Tea Party Patriots, one of several national tea party groups.

In truth, it is hard even for those who do give part of their salaries back to feel much glory from it. Walz said he was disappointed to learn that, because of the way the program works, his money wouldn’t cash out a single one of America’s IOUs.

“It would have made me feel good to see them buy back something with it,” Walz said. “You know, a piece of a bond, or something.”

Staff researcher Lucy Shackelford contributed to this report.