Breaking Verbal Rental Agreement

[Anthony Knippers]

Hi there

My wife and I are both new to renting properties and have an issue. We advertised our property and had plenty of people want to rent it but it went nowhere. We had an individual come look at the property and they wanted to sign a rental agreement on site. We we’re reluctant because we hadn’t verified income yet. We told them we’d be in touch. My wife exchanged text messages with them and told them we’d like to rent to them but needed to verify income. We had other people interested in the property, and we had an individual come look at it a day or two later with all their ducks in a row. They had proof of income on site and we’re ready to move forward. We physically signed an actual rental agreement with them and notified the other person immediately after. 
This individual is now threatening to sue us for violation of contract. We never collected deposits and she hadn’t sent verification of income until after we told her we rented to somebody else. We had plans to meet the following day and go over everything, but we jumped because this other individual was ready to go and had everything in order. 
My question is; Are our text messages considered a contract even though it never outlined when rents were due or any other variables, other than when she could potentially move in and what the security deposits would be? We never collected any money from them. Are there any grounds (in Oregon) for them to actually sue us?