United States Note
Options to reissue U.S. Notes have been proposed by both Republicans and Democrat s on several occasions, including the current Transportation Secretary when he was in Congress, Ray LaHood.  LaHood proposed reissuing $360 billion, roughly 100 times the last authorized amount - $346,681,016  - of Greenbacks when they were finally phased out in 1999, in order to rebuild transportation infrastructure. Although that bill was defeated, the fact remains that Congress can simply issue Greenbacks in any amount, at any time, for any reason. I have created a petition to encourage Congress to do so here: http://www.change.org/petitions/end-the-debt-crisis-with-debt-free-united-states-notes, which is also exhibit B in a lawsuit against Treasury wending its way through the courts, and more fully described here: http://www.opednews.com/articles/The-American-Crisis--To-F-by-Clifford-Johnson-120103-997.html 
Additionally, sole use of this kind of money is specified in Rep. Dennis Kucinich's bill, HR2990, based on Stephen Zarlenga's proposal from the American Monetary Institute.
It is telling that United States Notes are excluded from the debt limits, but in practice, this is a feature, not a bug, of United States Notes, since it allows this form of currency to be put to more productive use. A better, more productive way to inject this new money into the economy would be via public works jobs (we are still living off the great public works produced by FDR). The national debt can, in any case, be paid off indirectly through increased tax revenues resulting from growth and full employment, while the government ends borrowing, forever.
Double entry accounting, an accountant friend of mine assures me, is not a God-given law, or something without which financial accounting cannot function. This is no reason to stick with a system that must produce debt every time it produces money. We can split debt and money. FDR did it to a limited extent. Lincoln did it. Franklin did it. The Mint does it today with coins. Henry George recognized the inherent moral superiority of having the government produce money, debt-free, instead of a private banking cartel, or, conversely, of having "wildcat banking"  where dozens of regional banks and even private businesses like taverns, could produce their own money.
So, why not split the difference? Have government provide more money when needed, and for big, national projects that only government can do, but do it in a way that doesn't increase the debt.
To counter ever-rising levels of debt, provide full employment, and to create jobs for things that need to be done, Congress should create debt-free United States Notes.
Benjamin Franklin And the Birth of a Paper Money Economy By Farley Grubb, Professor of Economics, University of Delaware, and National Bureau of Economic Research - click hereben-franklin-and-paper-money-economy.pdfFindlaw.com -- a source for legal professionals - http://caselaw.lp.findlaw.com/scripts/getcase.pl?navby=case&court=us&vol=75&page=533
Henry George's concept of Money and Its Application to 21st Century Monetary Reform -- Concluding Remarks: Zarlenga, Stephen - http://www.progress.org/2003/moneyz05.htm
Julliard vs. Greenman - http://en.wikipedia.org/wiki/Juilliard_v._GreenmanJustica.com -- U.S. Supreme Court Center -- Legal Tender Cases, - 110 U.S. 421 (1884) -- Julliard vs. Greenman - https://supreme.justia.com/cases/federal/us/110/421/case.html
Lincoln's Populist Sovereignty: Public Finance Of, By, and For the People - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1489439 - Timothy A. CanovaNova Southeastern University Shepard Broad Law Center, January 1, 2009
Meaning and origin of the phrase "to coin" - http://dictionary.reference.com/browse/coin
The American Crisis: To Free a Lender-Owned Nation (Part 1) - Johnson, Cliff, Op Ed News, click here
The Coinage Clause in the Constitution -