Before the U.S. Treasury announced that it would be replacing the $10 bill (picturing Alexander Hamilton) there had been a substantial discussion in the blogosphere about the desirability of replacing the $20 bill (Andrew Jackson). The primary justification for replacing Jackson was his record as president, especially his opposition to the Second Bank of the United States and paper currency, but also his treatment of native Americans.
Many people may conflate Jackson's opposition to paper money with an opposition to Federal government participation in the creation or production of coin and currency. This is not correct. In the early part of the 19th century (and, indeed, until the Civil War), the Federal Government minted coins in various denominations (some examples are shown here; note that the gold and silver cins were much smaller than contemporary coins, so don't let the fact that they are all shown the same size deceive you. A silver dollar would have been about the size of a current dime. Jackson in fact supported coinage by the Federal government or gold and silver coins, and of "token" coins minted , for example, copper 1 and 5 cent pieces.
(That $1 gold coin would have been really tiny, and would weigh about 2 grams.)
Jackson's opposition to paper currency disguises, for modern audiences, his opposition to banks. In the early 19th century (and, indeed, even as late as the 1920s) paper money was issued exclusively (before the Civil War) or partly by private banks. And, before the Civil War, the banking business was largely the business of issuing bank notes (which were required to be, but were not always. convertible into gold or silver at a fixed rate (one ounce of gold was about $20; one ounce of silver was about $1.35). (Examples of bank note are shown here.
(I happen to have a $10 bill, issued by the Merchant's National Bank of Terre Haute in 1929, signed by the bank's Treasurer, my grandfather, Alfred J. Woolford.)
Banks today generate revenue (and profits) by accepting deposits (on which they may pay interest and may charge fees) and by making loans. How did banks in the 1820s generate revenue and make profits? Mostly they were not depository institutions; while savings and what we would call checking accounts existed, they were not terribly common. Banks made money by printing bank notes and making loans. Banks were generally required to redeem their bank notes with specie(gold or silver coins). Where, then, did banks get the resources to do this? [Today a large (but declining) source of funds for making loans is from deposits.) When a bank organized, its owners would provide capital, generally in the form of gold or silver coin or U.S. Government bonds. [The bonds also provided some income (interest rates on long-term US Government bonds averaged about 4.5% between 1820 and 1840).]
Banks could then make loans in one of two ways. They could provide a borrower with bank notes issued by the bank, with a repayment (including interest) as indicated by the loan agreement. The second mechanism for lending was a letter of credit, by which a bank would guarantee that any purchase for which the holder of the letter of credit used it would be made by the bank. Generally, banks charged a fee for issuing these and then charged interest on any amounts advanced. (Letters of credit could be conveyed in whole to a third party, and circulate as, essentially, a form of money.) According to Howard Bodeman and Hugh Rockoff's research, interest rates on private sector loans between 1820 and 1840 were roughly the same as those on U.S. Government bonds. Banks, knowing that all the notes they issued were unlikely to be presented for redemption at once, generally lent more (sometimes much, much more) than they had on hand in coin. This is, in effect, "fractional reserve" banking, which is how commercial banks operate today.
Now suppose Jackson had triumphed, and paper currency--bank notes--had been forced out of existence. Now what would banks do? Well, they could still exist, and they might have transitioned into depository institutions more quickly than they did. More likely, they would have organized as before, with owners putting up capital in the form of gold and silver coin and Government bonds. They could have made loans by lending the physical coins they had. If this were all they did, they would be practicing "100% reserve" banking--a bank could only make a loan if it had sufficient coin to do so. This would restrict the quantity of loans, which, by itself, would tend to drive interest rates up. Banks, however, would have had an alternative--expanded use of letters of credit and other negotiable paper. The bank would provide the borrower with the instrument, for which the borrower would pay a fee and then pay interest on any portion of the line of credit created.
Whether the net effect of elimination of paper money have been a contraction of credit generally is uncertain, but my own guess is that it would have. As a result, interest rates would have increased, borrowing would have decreased, the US rate of economic growth would have declined as firms acquired less capital equipment and expanded less rapidly. Not my idea of the best possible outcome. But, then, Jackson is not my idea of the best possible president, on almost any dimension.
 Howard Bodeman and Hugh Rockoff'. "Regional Interest Rates in Antebellum America," Strategis Factors in Nineteenth Century American Economic History: A Volume to Honor Robert W. Fogel (ed. Claudia Goldin and Hugh Rockoff, University of Chicago Press, 1991, pp.159-187.