Under no circumstances should you ever consent to a search.
First, its your house or car. LEO has no business searching it.
Second, LEO's only job is to bust you. Do not make this job easier. There is frequently a feeling that arises that if you co-operate with LEO, things will go easier for you. Resist this feeling with all of your might.
Third, if LEO says "If you won't consent, I'll go get a search warrant," then tell him to go get his search warrant. In order to get his warrant, he must have probable cause that you have committed a crime and that there is evidence of this to be found in the area to be searched. Usually, LEO is bluffing. If he had probable cause, why is he asking you for permission?
Finally, even if you think your house or car is clean as a whistle, guess who will find that dropped roach or missing pipe. You guessed it, Johnny Law.