At some point in 2012, President Obama and his GOP opponent will formally declare whether they plan to take public funding for their general-election campaigns. If House Republicans get their way, there won’t be a choice to make.

This week, the House will vote on a bill sponsored by Rep. Gregg Harper (R-Miss.) that would abolish the Presidential Election Campaign Fund and the Presidential Primary Matching Payment Account. Any money left over in those funds would be sent to the U.S. Treasury to help chip away at the deficit.

(Harper’s bill also would terminate the Election Assistance Commission, a longtime goal of Republicans who argue that the body, established by the 2002 Help America Vote Act, has already fulfilled its purpose. Democrats strongly disagree.)

Created in 1976, the public funding system — which offers money to qualified primary- and general-election candidates, raised via a voluntary checkoff on individuals’ tax returns — has been on the ropes for at least a dozen years. George W. Bush started a trend by declining to take money during his 2000 and 2004 presidential primaries, and Obama became the first candidate not to accept funding for his general-election campaign in 2008.

At the same time, the proportion of taxpayers choosing to contribute to the presidential fund has been inching steadily downward. According to the IRS, the number has dropped from nearly 20 percent in 1990, to 12 percent in 2000, to less than 7 percent in 2010. So why continue a program that so few Americans are willing to subsidize?

“I don’t think that it’s necessarily done what it’s intended to do,” Harper said in an interview, referring to the idea that public financing would reduce the influence of special interests on the electoral process.

He said that in 2012, “it’s apparent that none of the perceived major candidates are going to take advantage of the system or money that might be available.”

Obama’s campaign did not respond to a request for comment, but there’s little reason to expect that he will take what the FEC offers for the general election — less than $100 million — when he already has demonstrated the ability to raise many times that amount.

When Obama opted out of public financing for the 2008 general-election campaign, he said it was “not an easy decision, and especially because I support a robust system of public financing of elections. But the public financing of presidential elections as it exists today is broken, and we face opponents who’ve become masters at gaming this broken system.”

Republicans at the time branded Obama a hypocrite for saying he supported public financing and then abandoning the system because he could raise so much more outside of it. Obama ended up bringing in more than $750 million overall, while Sen. John McCain (R-Ariz.) took $84 million from the FEC and ran at a severe financial disadvantage.

Another bill to end public funding for presidential campaigns, sponsored by Rep. Tom Cole (R-Okla.), passed in January with the support of all but one Republican present, as well as 10 Democrats. Senate Minority Leader Mitch McConnell (R-Ky.) introduced a companion measure in the Senate that never came to a vote.

The White House said then that it was strongly opposed to Cole’s bill “because it is critical that the nation’s presidential election public financing system be fixed rather than dismantled.”

The bill’s effect, the White House said, “would be to expand the power of corporations and special interests in the Nation’s elections; to force many candidates into an endless cycle of fundraising at the expense of engagement with voters on the issues; and to place a premium on access to large donor or special interest support, narrowing the field of otherwise worthy candidates.”

The administration did not specify how the system should be “fixed,” nor did the Obama campaign get into detail when it opted out in 2008.

But Reps. David Price (D-N.C.) and Chris Van Hollen (D-Md.) have proposed mending the system rather than ending it, offering a measure that would provide significantly more public funding for presidential candidates. The bill would lift the spending limit for general-election campaigns and allow recipients to keep taking private contributions of up to $500 per donor. And the current voluntary $3 checkoff on tax returns would increase to $10.

Both Price’s bill and Harper’s bill also would eliminate public funding for national party conventions. The FEC noted in early November that each side had applied for and received nearly $18 million to stage their conventions next year. That prompted Democracy 21, which advocates for stricter campaign finance laws, to accuse the GOP of hypocrisy.

“It is more than ironic,” the group said, “that at the same time Republican leaders in Congress are trying to kill the public financing system, the Republican Party is happy to ask for and accept public funds to finance its own political activities.”