You cannot reside in the U.S. on a tourist visa or Visa Waiver while waiting on a K1 Fiance visa or K3 Spousal visa. However, you can make a temporary visit using a B-2 tourist visa or on the Visa Waiver Program.
You will need to prove to the consular officer reviewing the application that you intend to return to your country when your tourist visa expires. The consular officer will consider the pending K1 or K3 petition as a factor and may deny your visitors visa if he is not convinced that you will return home. Even if you are issued a tourist visa, the immigration inspector at your port of entry can still deny your entry if he feels you do not intend to leave. For example, if you show up at the inspection station with a pending K1 visa and far more luggage than an average tourist would have, the inspector may suspect that you do not intend to return to your home country.
You can be denied entry even though you have a valid tourist visa.