THE Democrats trumpet the gains they've made ''reinventing government,'' and the Republicans rail against how big and unresponsive government is. While our politicians struggle and posture about shrinking government, they overlook a unique way to combat counterfeiting, which would in turn save taxpayers considerable money. Congress, the Treasury Department, and the Federal Reserve should seize this opportunity and create a new one-dollar circulating coin and eliminate the $1 bank note. The dollar-coin issue, however, is shrouded in myths. Myth No. 1: There is no savings to the government. That's nonsense. After listening to officials of the Congressional Budget Office and the General Accounting Office on July 13, Sen. Alphonse D'Amato (R) of New York, chairman of the Senate Banking Committee, said the public would be astounded if the government passed up a $400 million annual savings over 30 years. Federal Reserve Board Gov. Edward Kelley Jr. testified at that same hearing that the Federal Reserve would back a dollar coin, principally because of savings it estimated to be in excess of $400 million annually. Myth No. 2: The savings are suspect. Tell that to the Chicago Transit Authority. The CTA processes $123 million in paper currency each year. It could save $2 million to $4 million annually in processing costs if it did not have to cope with dollar bills. Officials of the Southern California transit system say eliminating the dollar bill would allow them to put 24 new buses on the freeways without raising fares. Myth No. 3: The Susan B. Anthony dollar too closely resembled the size of the quarter. The Susan B. Anthony was, in fact, 40 percent larger. It did resemble the quarter in some ways, but if its color were changed and its edges not reeded, the coin would have a clearly distinguishable heft and appearance. Myth No. 4: The public won't accept a dollar coin. The problem is, Americans haven't yet learned of the savings and ease of using a dollar coin. People only carry an average of three dollar bills at any given time. They won't be weighed down by a large number of dollar coins. In fact, they will carry even fewer quarters and use $2 bills. Myth No. 5: The vending-machine industry would use the dollar coin to increase prices. Governor Kelley of the Federal Reserve Board gave this example to demonstrate the fact that the United States is based on a competitive, free-market economy. He related how he likes to get up from his desk on some afternoons and walk to the basement of the Fed, where there is a long line of vending machines. A few months ago, a store opened up about 20 feet from the vending machines. Soft drinks at the store were sold for 50 cents. Within two weeks, the price of a soft drink in the vending machine dropped from 55 cents to 50 cents. The government must stop printing the $1 bill if a dollar coin is to be successful. One-dollar bills represent 47 percent of the annual production of bank notes printed by the Treasury Department's Bureau of Engraving and Printing. The government will need that volume to replace the $350 billion worth of currency notes in circulation - particularly to combat counterfeiting abroad, most of which is in higher denominations. If the US mint needs production facilities to produce a dollar coin, it could eliminate the one-cent piece, which constitutes 79 percent of its production. Alternatively, the mint could privatize the production of pennies. Let's shatter the myths surrounding the dollar coin. Let's grasp onto the major savings a dollar coin would provide.