Which part is orange? Is it the cabinet or the countertop? If it's the cabinet, painting it should be pretty easy--just sand it a bit, prime, and paint. If it's the top, it's harder, but doable. I had an ugly vanity in my bathroom too, and I painted it as follows:
1) masked off the sink and cabinet
2) scuffed up the laminate with sandpaper
3) applied a primer
4) gave it one coat of a basic acrylic paint and let that dry
5) sponge-painted over it in a second color to give it some texture
6) applied three coats of water-based polyurethane over that to protect the finish
For the most part, it has held up pretty well. It has sustained a little bit of water damage in the area right under the soap dish--water was left standing on it, and the paint underneath got sort of wrinkled. It doesn't show too badly, and I now take care to wipe up spilled water promptly.
However, if this sounds like too much work, replacing the top may not be too expensive. Check the prices at Lowe's or Home Depot (or at your local Habitat ReStore if you have one in your area). You may find you can simply replace the whole top for under $100. Or, you might be able to re-laminate it.