You cannot reside in the United States on a B-2 tourist visa or on the Visa Waiver Program while waiting on a K1 fiancé visa or K3 spousal visa. However, you can make a temporary visit on those visas.
You will need to prove to the consular officer reviewing the application that you intend to return to your country of residence when your tourist visa expires. The consular officer will consider the pending K1 or K3 petition as a factor and may deny your tourist 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.
If you do enter the country for a visit, you will need to leave before the end of your stay.