A photosynthesizing mouse?
It is almost impossible for following reasons:

For photosynthesis you need chloroplasts
To maintain chloroplasts you need many genes in the nucleus that will support its endosymbiosis

I said almost impossible because there are some natural examples of what you are asking. A sea slug called Elysia  acquires choloplasts from green algae on which it feeds. However, it cannot maintain the chloroplasts and pass them on to the next generation but it acquires enough to appear green and survive on photosynthesis when there is no food.
Another example is that of the protist, Rhopalodia gibba, which acquired a cyanobacteria like organism. This protist already had a red alga derived secondary plastid before it acquired a &quot;green&quot; cyanobacteria. This acquisition gave the host the ability to fix nitrogen in the presence of light.
The case of Paulinella chromatophora is very interesting because the acquisition of an endosymbiont happened very recently. The endosymbiont is close to Synechococcus clade of cyanobacteria.
Intuitively, it can be understood that these kinds of acquisitions would be quite difficult for a multicellular organism.
ADDENDUM
Photosynthesis is a complex reaction which requires a dedicated compartment which not only harvests light and produces ATP but also has enzyme complexes required for anabolism (carbon fixation etc).
For now we can accept the hypothesis that it would not be possible for a huge eukaryotic cell to perform these functions in absence of a dedicated organelle. For a discussion on why this is so, you can refer this post.
Having said that, there is an easy way to impart partial photosynthetic ability to a eukaryotic cell. Some archaea and bacteria employ rhodopsin to pump out protons against its gradient, in the presence of light; this is coupled with ATP-synthase just like the complexes of ETC in mitochondria. In this study, Hara et al have expressed delta-rhodopsin in mammalian mitochondia which now makes the mitochondria generate ATP in presence of light. Furthermore, these cells were immune to mitochondrial toxins that affect complex-I activity.
PS: thanks biogirl. I almost forgot about this and I just remembered when I was reading about something else