Can I travel to Brazil and back from the US with an expired Brazilian passport?

The question of whether you can enter Brazil with your expired passport has already been answered here on Travel.SE - Can I return to Brazil with a recently expired passport?

However returning to the US will be a different matter. According to the Brazilian Consulate in Houston website :

Brazilian citizens, even those with dual citizenship, must enter and leave Brazil with a Brazilian passport.

So you're fine to enter Brazil, but not to leave.

Your options are either to obtain a new Brazilian passport (either in the US or Brazil), or to renounce your Brazilian citizenship, at which point you will be able to travel with your US passport.

It appears that you'll be OK to travel to Brazil. From Timatic (italics mine):

Destination - Brazil (BR)

Passport

Passport required.

Passport Exemptions:

Nationals of Brazil with a national ID card . Nationals of Brazil with an emergency passport.

Document Validity:

Nationals of Brazil are allowed to enter with an expired passport.

When nationals of Brazil travel with an emergency passport, a Laissez-Passer issued by Brazil or a national ID card, it must be valid on arrival.

...

Transit - Panama (PA)

TWOV (Transit Without Visa): Passengers with a confirmed onward ticket for a flight to a third country within 12 hours. They must stay in the international transit area of the airport and have documents required for the next destination.

You'll need to carry both of your passports to prove to the airlines' satisfaction that you'll be admitted to Brazil upon your arrival.

Edit: The return trip is dicier. If you can get to the departure gate, the airline will probably let you board, as a US passport is sufficient to travel to the US via Panama.

However, as pointed out by Doc's answer, Brazilian law requires Brazilian citizens to enter and exit the country using a Brazilian passport. If you attempt to conceal your Brazilian citizenship from the Brazilian exit officers, your US passport will not have a valid visa or entry stamp from your visit, which will raise questions. (One way to get around this would be to renew your passport while you're there, which would obviate the whole problem.)

Upon your return, you should be OK traveling on your US passport alone. However, if there are exit controls upon leaving Brazil, you may need to show them your expired Brazilian passport to prove that you entered the country legally.