My question is, will I be given any problems, detained and forced to miss a flight I will undoubtably have to make back to the states, if I try to leave China on an expired visa within 10 days of it expiring?

You will probably be prevented from travelling on that flight. The authorities will want to deal with your overstay first of all. That'll take some time, a day or two to sort out.

If you wish to buy an air ticket to exit China on a particular date, the travel agent will check your passport first to see whether you've overstayed at the time you visit his office, or will have overstayed by the date of your planned departure. You'll only be able to purchase such a ticket if no overstaying has occurred already, or will have taken place by the time you plan to leave China.

If you've overstayed already, visit the PSB ASAP, and carry enough cash with you to pay a fine of 500 Yuan per day of overstay up to a maximum of 5000 Yuan for 10 or more days of overstay plus around 200 Yuan to pay for your new 10-day * visa. Once you've got said visa you can buy your travel ticket for an exit date before your new visa will expire.

Better to visit the PSB on the last day your present visa is valid, and apply for an extension. By doing so you may be able to get a 10-day visa without the * for about 200 Yuan, and not be fined. Then arrange to travel on a date before said visa expires.

Either way, you may not have to return to the States if you can get a new Chinese visa in Hong Kong, for example. Consult visa agents there to see if that is possible in your particular case.