Self Priming Paint
Is this possible with house paint?

Very few products can be considered self priming and most paints are not a part of this category. Primer plays a very important role in providing a stable foundation for the house paint.

A high quality primer can do many things paint can't.

Bonds a surface, making it more stable.
Can penetrate below some questionable surfaces. Helping, by acting like glue.
Seals the surface and blocks stains from bleeding threw the paint.
Increases the coverage of the paint. Making vivid colors cover better in fewer coats.
Can be sanded smooth. Difficult with paint, depending on the type.
Makes the house paint last longer.

House paint is the finish and color. Primer is the foundation to any great, long lasting house painting project.

Some manufactures claim that their paint can act as a primer, in other words binding to surfaces like a primer. At the same time they manufacture primers. Why sell a primer if it's not needed? This sounds like a sales pitch to increase the purchase of a particular product.

The only self priming paint I'm aware of is specialized industrial finishes, like floor epoxy and Direct to Metal, DTM, finishes. Even these products have primers designed to increase overall performance.

The idea that house paint can be self priming is questionable. I recommend using the appropriate primer. Now is the only time you will have to do it right. The amount of time and money spent now will save much more in the future.