Can a Car dealership cancel a contract and Bill of Sale in Colorado?

We went to a Honda dealership and was their for six hours trying to get a vehicle. Our credit is not that great so they wanted a big down payment. We had $2400 to put down that day, $600 more than what they told us over the phone what would be ok. Our total income is about $7400 a month. About $1200 a month is from natural gas royalties. But on the app. We put total income as $7160. They said the bank wanted $4400 down so we can get the car. We didn't have all the money at the time, so they said they would give us 3 weeks to get the other $2000. So we cut a check for $2000 and they said they would deposit in 3 weeks. We have had it for 12 days and now they call and said they need another $2440 along with the $2000. So for a total of $6840 for the down payment. The car is a 2011 Honda touring. They gave us Bill of sale paper, dmv papers, along with retail installment sale contract on how much and when we start paying. They said they need to know today or they are going to get the car. Can they do that?

Yes they can. Auto loans are collateral loans, and failing to pay according to your contract will result in loosing your car

As you may know, dealers have to try to find you financing with the banks and finance companies that they work with. If your credit is bad, they can have problems getting anyone to finance you at the original terms that you agreed to. With different terms, such as a larger down payment, he might find someone to finance you. Until then, he hasn't been paid for the car, it still belongs to him, and if you can't agree to the new terms, he'll want his car back.

Yes they can, but the other side of the coin is that if they change the terms on you and you are unable or unwilling to meet those terms, you can walk away and get all your money back.

Yes, And you will probably be better off without it. I suspect you were getting hosed badly. So bad the lender wouldn't allow it.

Yes they can do that. It's not right but they never qualified you for that loan so nothing is final. They strung you along. You should have NEVER agreed to lie about your income on the application. Thats called bank fraud. If they are willing to commit fraud just to sell a cat, that is the first indication they aren't trustworthy.