Much has been made of issuing a "trillion dollar platinum coin" as a part of a solution for the current budget crisis. While such an action is possible it will produce monetary outcomes which are significantly different than if the government sold an additional $1 trillion in bonds as it usually does to finance its deficit spending.
The difference comes down to what is money? In the case of the US it is the US dollar. A bond, while having value and a use in exchanges, is not money. Thus, adding bonds to the market does not increase the amount of money in circulation. Adding $1 trillion does add to the money supply. But the change to the money supply does not end there. The US banking system is a fractional reserve system in which the vast majority of money is created not by the government, but by the banks.
Under a fractional reserve system the amount of money is largely determined by the so called money multiplier, which is derived from the reserve requirements in effect at the time. Currently, this is about 10% of deposits, which indicates that the money multiplier is about 10x the amount of the monetary base. This mean that for every dollar of monetary base, or high-powered money, the total money supply (M1) will increase by 10 dollars through bank lending. The monetary base is created by the government mostly through the purchasing of bonds by the Fed.
The issuing of bond by the government doesn't change the money supply, but the issuing of a trillion dollar coin not only changes the money supply directly, but induces a multiplier effect because the trillion dollars will add to the monetary base. Therefore, the trillion dollars deposited in the treasury account will add 10 trillion dollars to the money supply (M1) as the government spends that money. This won't happen immediately, as the government won't actually spend that trillion dollars at once, but will leak into the financial system as the government uses those funds to pay its bills.
This addition to the money supply is, of course, of crucial interest to the Fed as its job is to regulate the money supply. It could react to the addition to the monetary base in many ways. 1) it could reduce its own purchases of bonds, 2) it could increase the reserve requirements such the the money multiplier is reduced from the current value, 3) it could use its recently formed mechanism of paying interest on reserves held at the Fed by banks to induce the banks to leave the extra money in their Fed accounts so as to not lend it out.
One important benefit to the government of issuing the trillion dollars is that it won't have to pay interest on it as it would if it had issued a trillion dollars in bonds. This adds up to a big savings for the American people over time.