The short answer? Almost definitely not.
The estate tax, sometimes called the "death tax," is often cited by politicians and commentators, but it's rarely explained. The thing you need to know is that the US estate tax only applies to people whose estates are worth more than $5 million. Most Americans simply don't have estates that are worth that much money.
If, however, you're worried your estate might qualify for the tax, that's all the more reason to speak with an established estate planning attorney and create a Trust. Remember: a $5 million estate doesn't mean that you have $5 million of liquid assets. Rather, you may qualify if you own valuable property or own a promising and growing business.
Unless you're survived by your spouse, estate law in the U.S. doesn't require your beneficiaries and heirs to pay down your outstanding debt. Of course, that doesn't mean your estate itself will be let off the hook.
Basically, if you leave behind large bills or mortgages or other debts (such as to creditors or business partners) your estate itself will foot the bill. A court may order your assets liquidated (such as the selling of property to pay off existing loans) but your friends and families won't be reaching into their own pockets to pay anything you owed personally.
That's why it's important for you to do your best to settle your outstanding debt if you're planning on leaving your assets behind. Sometimes, a Trust can help preserve especially important (or sentimental) property from creditors, but asking an estate planning attorney will help you make sure that your heirs get what you want them to.