Bruce Bartlett highlights the GOP ploy as a way to reemphasize the need for higher taxes on the rich:

Recognizing the intellectual and political weakness of their position, Republicans have responded that there is nothing to stop rich people from sending checks to the Treasury Department to reduce the debt. About $3 million is annually donated to the government for this purpose. On Oct. 12, Senator John Thune, Republican of South Dakota, introduced legislation that would add a line on tax returns to make voluntary contributions to the Treasury. It was enthusiastically endorsed by the anti-tax activist Grover Norquist.

Reducing the deficit through voluntary contributions is not a serious idea. It would be a drop in the bucket, such contributions are not sustainable, and it would be unwise to have the government dependent on them because inevitably they would come with strings attached.