My question involves landlord-tenant law in the State of: Utah

Me and my boyfriend moved in with his close friend and his girlfriend in June. I've never lived on my own or with roommates before so this was a cool idea to me, like a soft trial run of being on my own but kind of not. We didn't really have many options as we were living with my boyfriend's mom who passed away very suddenly. So we moved from California all the way to Utah under the impression that we could live here "two years, three years tops though." We didn't have much money and were told we would have to pay a hefty pet deposit of 1,500 dollars. We scrimped and saved and came up with the money. 700 in cash, the rest needed a trip to the bank. We tried to give them this money repeatedly at the beginning but the landlady hadn't contacted them about resigning the lease so they told us to keep it.

I tried to find work but nothing came up and eventually we needed to pay rent that we didn't have. We dipped into the pet money. It was wrong and stupid, but we had nothing else. We told them we were doing this but they said nothing against it (such as "we're resigning the lease next week so that'd be dumb but it's on you"). Another month goes by and we hear nothing about the pet money. Finally we ask and they say the lady hasn't gotten back to them and "not to worry about it" that it might not even come up. Eventually we had an incident where a doctor trip was needed so we dipped again. I eventually found a job in October but almost all of our money was going to rent/utilities or food, and just a little tiny bit towards Christmas. Things were starting to look up though as the holidays were ending, and I was planning to go into saving mode, thinking we had time. I'd save all summer and maybe get some money back from taxes, have the cat money in the bank if needed and plus a little more by the end of summer. But then suddenly my boyfriend's friend said that they weren't resigning the lease in august so we needed to talk about moving before then and about this pet money. It was right before Christmas and before they were going on a short trip for New Years, and I was working at odd hours so the opportunity was hard to find to talk. However we told them any time was good for us as long as we all were home and we were all always around on Sunday.

Today the girlfriend came in and told us we either needed 1,500 by the first of February or we needed to move by then. That's less then thirty days to either make 1,000 dollars or move. I don't think I can manage either in so short of time. We aren't on the lease and we do have pets here without having paid that money, but I feel like this whole thing is really shady. They as our landlords technically let us stay without paying the pet fee. We never signed anything though, but I would have paid it either right when I had it or saved up a little better if they hadn't said not to worry about it.

I'd rather put my energy into moving as it stands but I just don't have the means to do that in twenty-four days. Is there any possibility where we might be able to stay a tiny bit longer? Some kind of rule or law that might help? I just need a little more time than they're giving me or am I completely screwed due to the pet thing?

Edit: I guess telling us they want us out is some kind of notice, but it isn't really official. They didn't write it down and it didn't feel like a hard date and her boyfriend wasn't even here and he is the whole reason we chose to move here at all.