Fitzpatrick's bill would also make it the general policy of the government to replace paper dollars with dollar coins "after $1 coins achieve sufficient market penetration such that consumers and retailers are comfortable using $1 coins and are able to obtain adequate supplies of $1 coins."

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The Fed would have to continue to remove "unfit" currency from circulation, and be required to "continue to destroy such currency."

Members have proposed abolishing the paper dollar several times over the last few years. Supporters see it as a way to save money — the Government Accountability Office has said millions of dollars would be saved by doing away with the more perishable paper dollar.

But the issue has drawn opposition. In 2011, then-Massachusetts Sens. Scott Brown (R) and John KerryJohn Forbes KerryBringing the American election experience to Democratic Republic of the Congo Some Dems sizzle, others see their stock fall on road to 2020 The Hill's 12:30 Report MORE (D) proposed an alternative bill meant to protect the paper dollar from the "massive overproduction" of the "unpopular $1 coin."

Supporters of the dollar coin pointed out then that Massachusetts-based Crane & Co. is the sole-source supplier of paper used to make dollar bills.

Among the co-sponsors of the last Congress's bill were Reps. Kevin BradyKevin BradyOvernight Finance: CBO to release limited analysis of ObamaCare repeal bill | DOJ investigates Equifax stock sales | House weighs tougher rules for banks dealing with North Korea Week ahead in finance: Clock ticking for GOP on tax reform Liberal groups want Mnuchin off GOP tax group following airplane controversies MORE (R-Texas), Trent FranksTrent FranksGOP rep: North Korea wants Iran-type nuclear deal Debt-ceiling gambit stirs GOP debate GOP rep shares story of brother with Down syndrome, condemns abortions MORE (R-Ariz.), Walter Jones (R-N.C.), Greg Meeks (D-N.Y.), Pat Tiberi (R-Ohio) and Paul Tonko (D-N.Y.), all of whom are co-sponsors of Fitzpatrick's bill this year.