Multiple-entry Brazilian Tourist Visa for US citizen without flight tickets set

EDIT As per your comment, you will not have the issue of excess duration, since you are staying less than 90 days, so only matter of getting a return flight.

What you need to do then is to choose a way to satisfy the return flight requirement. You have three options as far as I know:

• A fully refundable ticket. This is normally purchasable from the airline. This is the option to use if you are not returning by air.
• A changeable ticket. Many airline tickets can be changed for a fee, usually $100-$150 USD or so. Simply buy such a ticket that is at most 90 days from your scheduled arrival in Brazil. When you figure out when you are flying out, call the airline and change the departure date for the said fee.
• Get a website to buy the refundable ticket for you. For a fee, some websites will buy the ticket, send you the booking information and then cancel it within 24 hours. You can use this if your credit-card does not have enough funds for the other options. I have never done this but I know people who did. There is a risk that someone may check and see that you are no longer booked when processing your visa application, so I would save that as a last resort.

EDIT Should you want to stay more than 90 days, things get more complicated. I know you said it does not apply to you but I think this is useful information for others or if you change your mind:

The longer stay is the tricky bit. A Brazil visa is usually valid for 90 days per visit but you are allowed to apply for an extension from the Federal Police in Brazil which can let you stay up to 180 days. The real problem is that the airline will be extremely reluctante to let you fly in if your return flight is not 90 days away since the visa printed in the passport clearly states you are allowed 90 days per visit. So, you will have to get a refundable flight which you will know that you cannot use.

Just last year I went through the whole process. I had a return flight 6 months way but the airline would not let me check-in easily. It took taking to 3 check-in agents and 2 managers for 90 minutes (!!!) while every other customers were waiting in back of us. I mostly kept repeating and quote the official rules saying that the visa is extensible once there. They copied all my documentation and made a case file, whatever that means to them I do not know, in case they would be fined for flying me there should I be denied entry.

The other justification letter I had to write was regarding lodging. I only had the first 7 nights of hotels booked at my arrival city since I wanted to explore much more of the country but I had not managed to get the internal flights yet. With that, they did grant me the visa and it took only four days, although the embassy says to allow up to 90 days.