The Bad
The main worry about deficits is crowding out. Crowding in was just described ?€" it occurs when deficits cause output to go up and business confidence is increased. Crowding out comes about when deficit spending raises interest rates. There is a limited amount of funds available for investment, and when government competes with the private sector for a share of these funds to finance its deficit spending, it drives the cost of these funds ?€" interest rates ?€" higher. The increase in the interest rates causes investment to fall, and lower investment translates into lower output and lower economic growth. In addition, to the extent that the private sector is more efficient than the public sector, crowding out, i.e. more government spending and less private investment, can result in a less efficient use of resources (though in the case of public goods government can be the more efficient provider, and hence it is not always the case that efficiency falls).
Another worry about deficits is that they will be monetized leading to inflation. Debt monetization occurs when the Fed prints new money and uses it to purchase government bonds help by the private sector. This removes debt from the private sector and replaces it with money, and if the money is used to purchase goods and services, as it's likely to be, this can be inflationary (though when there is an excess supply of goods, as in a deep recession, inflation is unlikely to be a problem).
The Ugly
The worst outcome would be for the deficit to get so bad that the government chooses to default on debt payments (which could also lead to some other currency, or a basket of currencies, replacing the dollar as the vehicle and reserve currency). I don't expect this to happen, particularly since we can always print money to pay off our debts. But printing money to pay off debt could be highly inflationary, it could lead to high interest