Both Chihuahuas and Dachshunds are prone to joint problems because their conformation, short legs that are often twisted rather than straight tends to put more stress on their joints.
They are also prone to intervertebral disc disease. This is when the spongy discs between the vertebrae in the spine either prolapse or leak and put pressure on his spinal cord. If the affected disc is in the neck this pressure can affect the nerve roots to his front or all four legs and his neck. If the affected discs are in the back then the rear legs and muscles of the back are affected. This is quite painful and can lead to painful muscle spasms or if there is enough pressure then even paralysis can result. They walk stiffly and refuse to jump/climb stairs because it hurts and they don't feel as strong as they usually are.
At this point whatever his injury may be I recommend keeping him very quiet, no running, jumping or bending over (elevate his food and water bowls to head height) is best.
If you have a crate for him I highly recommend using it. The less he moves around the more comfortable he will be and the faster he will heal. He should go out on a leash to relieve himself. Do not use a collar for him, a harness which more evenly distributes forces if he pulls on his leash is better.
These don't heal quickly, they can take weeks or months to heal. You may need to confine him for several weeks, even as he starts to feel better or he may reinjure himself. Keeping him on the thin side is recommended to decrease stress on his neck and joints, but is no guarantee that he won't have another episode. Once a dog has one bad disc or joint pain the likelihood of another episode is very high.
If you are interested in reading more here is a link to an excellent article about intervertebral disc disease, its causes and therapy: http://www.petwave.com/Dogs/Dog-Health-Center/Bone-Joint-Muscle-Disorders/Intervertebral-Disk-Disease/Symptoms.aspx
Long term for any joint pain I recommend using a combination of a glucosamine/chondroitin product (examples are Dasuquin or Cosequin) and an omega 3 fatty acid (like 3V Caps or Derm Caps). I recommend an omega 3 fatty acid dose based upon the EPA portion (eicosapentanoic acid) of the supplement as if we do that the rest of the supplement will be properly balanced. Give him 20mg of EPA per pound of body weight per day. For example a 15 pound dog could take 300mg of EPA per day.
Omega 3's and glucosamine/chondroitins work synergistically and improve cartilage health and joint fluid quality and quantity as well as reducing inflammation. They can take several weeks to see full improvement. They are available over the counter.
Another option is a product called Duralactin. This is an anti-inflammatory product derived from milk proteins and it also has omega 3 fatty acids incorporated into it which can be very helpful. See this link for further information: http://www.duralactin.com/products_canine.htm
I suspect that his veterinarian prescribed a nonsteroidal (like Metacam, Deramaxx, Previcox or Rimadyl.) If those aren't enough to get him comfortable we can add another drug in the opiod family called Tramadol and/or another drug called Gabapentin.
You can also try alternating warm and cold packs on his painful back muscles for 10 minutes at a time several times a day. Heat reduces painful muscle spasms and cold reduces inflammation.
I suspect he isn't passing stools because it hurts to crouch or he is having trouble holding a crouch position. That should improve over the next 24 hours or so.
If we cannot control pain with medications and rest sometimes surgery is the only option.
Please let me know if you have any further questions.