It's been done before, and has several benefits.
In the United Kingdom, for example, whenever you buy or sell a share of stock (or a credit swap or a derivative, or any other activity of that sort) you pay a small tax on the transaction. We did the same thing here in the US from 1914 to 1966 (and, before that, we did it to finance the Spanish American War and the Civil War).
But there are other benefits.
As John Maynard Keynes pointed out in his seminal economics tome, The General Theory of Employment, Interest, and Money in 1936, such a securities transaction tax would have the effect of "mitigating the predominance of speculation over enterprise."
In other words, it would tamp down toxic speculation, while encouraging healthy investment. The reason is pretty straightforward: When there's no cost to trading, there's no cost to gambling. The current system is like going to a casino where the house never takes anything; a gambler's paradise. Without costs to the transaction, people of large means are encourage to speculate - to, for example, buy a million shares of a particular stock over a day or two purely with the goal of driving up the stock's price (because everybody else sees all the buying activity and thinks they should jump onto the bandwagon) so three days down the road they can sell all their stock at a profit and get out before it collapses as the result of their sale. (We ironically call the outcome of this "market volatility.")
Investment, on the other hand, is what happens when people buy stock because they believe the company has an underlying value. They're expecting the value will increase over time because the company has a good product or service and good management. Investment stabilizes markets, makes stock prices reflect real company values, and helps small investors securely build value over time.
Historically, from the founding of our country until the last century, most people invested rather than speculated. When rules limiting speculation were cut during the first big Republican deregulation binge during the administrations of Warren Harding, Calvin Coolidge, and Herbert Hoover (1921-1933), it created a speculative fever that led directly to the housing bubble of the early 20s (which started in Florida, where property values were going up as much as 70 percent per year, and then spread nationwide, only to burst nationally starting in 1927 as housing values began to collapse), then the falling housing market popped the stock market bubble and produced the great stock market crash of 1929. That speculation aggregated enormous wealth in a very few hands, crashed the housing and stock markets, and produced the Republican Great Depression of 1930-1942.
Franklin D. Roosevelt, as part of the New Deal, put into place a series of rules to discourage speculation and promote investment, including maintaining - and doubling - the Securities Transaction Excise Tax. Other countries followed our lead, and the UK, France, Japan, Germany, Italy, Greece, Australia, France, China, Chile, Malaysia, India, Austria, and Belgium have all had or have STETs.
Perhaps the most important benefit of immediately re-instituting a STET in the USA, however, isn't that it would raise enough money to bail out the banks and billionaires (and after that crisis is covered, could pay for a national health care system), or that it would encourage investment and calm down markets. Those are all strong benefits, and absent the current Republican Administration bailout proposal would stand-alone strongly.
But the Republican Bush Administration is currently suggesting that we borrow $700 billion (or more) from China and Saudi Arabia and other countries and investors, add that to our national debt, and repay it with interest (making the actual cost over the next 20 years over $1.4 trillion). This is what Republican Herbert Hoover tried in 1931 when he first created the Reconstruction Finance Corporation (later totally reinvented by FDR) to bail out the banks in 1931. Hoover's RFC bailed out the bankers, paid off huge salaries in the banking and investment world, bought him a few months (maybe that's the real goal of the Bush/McCain Republicans now - just hold things together until after the elections), but ultimately led to the failure within two years of virtually all the banks in the United States. The bailout failed.
Similarly, in 1998 the Japanese banks were facing a serious crisis of liquidity as the result of a bursting housing bubble in that country. The Japanese government used public funds to re-float a number of large banks that year, and it similarly failed. In one example out of dozens, in 1998 135 billion Yen were given from public tax funds to Ashikaga Financial Group, but the company limped along for a few years and in November of 2003 collapsed again, requiring a second infusion of a trillion yen from public coffers. And, as the BBC reported in a 30 November 2003 article ("Japan Bank Bail-Out 'A One-Off'"): "But experts warn that Ashikaga could be just the tip of the iceberg." Professor of Finance at Tokyo University Takehisa Hayashi said, "It will come as no surprise if we see another Ashikaga case in the near future." And they did.
Japan continues to limp along, as a result of bailing out banks rather than fixing structural problems. (At least the Japanese had enough savings to use their own money, instead of debt, to bail out their banks.)
So bailouts don't work, and never have. And they also have the side effects of damaging a nation's credit, sucking up its taxpayers resources, and (when done with debt) weakening its currency.
So let's go back to what we know works. After Hoover's 1931 bailout of the banks failed, FDR did a cold reboot of the entire system, putting into place strong rules to prevent speculative abuse. And he doubled the STET tax, both producing revenue that more than funded the Securities and Exchange Commission and further prevented a repeat of the speculative bubble of the 1920s that led directly to the Republican Great Depression.