Don't hate me for posting the opposite of most on this topic. To start off, I have to say that I am a current LEO that works for a city department, so perhaps I have a different perspective. Someone in a previous response asked for an LEO to comment. Sorry in advance to offend, if it does.
I have to say, that if I were in the same situation, I would have allowed the police to search, even if I wasn't a police officer. I'm somewhat saddened that law abiding citizens no longer trust the police. I assumed that the police took an oath to serve and protect, and to keep people safe. To hear that the police are not trusted by law abiding citizens, I feel that it pins "good against good". I believe we should be on the same team. I understand the issue with constitutional rights, and police have to abide by that. I strongly feel that the police are also here to PROTECT our constitutional rights, and I think about that issue every day when I go to work. I truly hope that every other LEO does the same.
I have absolutely nothing to hide, and nothing illegal in my house. Where I live, I have not heard of, or met a "dirty" cop. Maybe I'm in the minority. Sure, you hear the criminals say it all of the time, but I tend not to trust their information. I look at this way. If you have nothing to hide, and you believe they are really the police, and you are not concerned about them planting evidence (which where I'm from the police have more important things to do), then by allowing them to check the house for drugs or whatever, you are satisfying their concerns. Yes, I know it's a choice, but if the OP feels the same as I, he did nothing wrong. It's a choice for all of us to make, and respected either way. My thought is that he just gained a lot of trust from the police. Unfortunately, there is becoming this Us Vs Them with society and the police. Even with paranoia by perfectly law abiding citizens.
My perspective is that if you tell the police to take a hike a get a warrant, it could be perceived as you hiding something from them, therefore playing into the belief that you are doing something illegal. Based on what information they had, a warrant could actually get approved, and I would assume they would be looking much harder for drugs than if voluntary consent was given. Probable cause is what is required to get a warrant, and there are too many variables to say what PC is in this case. Each case if unique, as well as each judge that's approving the warrant.
Again, I'm not saying that you should allow the police to enter your home and tear it apart, but I see no harm in allowing them to look around. In my state, there is an issue of Ferrier Warnings, where if you agree to a search, you may limite the scope of the search, and deny further searching at any given time.
I'm happy that the OP felt comfortable enought to trust the police and allow a search. Long winded, I know. I'm done with my rant.