The Government Accountability Office, a bipartisan congressional watchdog, has produced five reports in the past 20 years to support the transition to $1 coins. Its last report, in 2011, said the government could save $5.5 billion, a conservative estimate according to advocates.

"It seems to me this one common-sense remedy certainly won't change the equation entirely. But even in this town, $5.5 billion or $13.8 billion is not chump change," said McCain, a Republican of Arizona.

McCain has been joined in his legislative push for the coins by fellow Republican senators Tom Coburn, of Oklahoma and Mike Enzi of Wyoming, as well as Democrats Mark Udall of Colorado and Tom Harkin of Iowa.

But they will have a hard sell. Even though most other countries, such as Canada, Britain and Japan, have replaced smaller currency denominations with coins, Americans love their greenbacks and have never warmed to dollar coins.

Maybe it's because many of us are in the habit of chucking coins in a jar or a piggy-bank. Maybe we don't like their bulkiness in the pocket, or perhaps that vending machine won't accept them. The reasons may not always be clear, but we just don't like them.

It began with the original gold dollar in circulation from 1849 to 1889, which was tiny, making it difficult to grasp and easy to lose, a serious problem when a dollar was almost a day's wage.

So the Mint made them bigger, but many people didn't like the idea of heavy coins filling up their purses or making holes in their pants pockets. Then there was the Susan B. Anthony dollar, which was introduced in 1979. It was often confused with the quarter, because it was roughly the same color, size, and design.

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That coin was never popular and was quickly discontinued in 1981, but resurrected in 1999 when Treasury reserves were low. It still never caught on. Neither did the later Sacagawea dollar coin, which was used mostly as change in vending machines, most often in transit systems and post offices.

This dislike of coins by Americans contrasts with currencies of most other developed countries, where denominations of similar value exist only in coin. These coins have largely succeeded because of a removal of their corresponding paper issues. But the U.S. government has taken no action to remove the one-dollar bill, due to intensive lobbying.

—By Steve James, NBC News

