Hello Vicki, I'm Dr. Deb. I'll do my best to help you today.
I'm sorry for this concern for your Dachshund.
I suppose it's possible that he could be constipated although this particular problem doesn't tend to happen as frequently in dogs as it does in cats. If the stool which was adhered to his fur was really firm/ hard and/or he was straining to produce his stool, then this might be the problem.
One way to know for sure, if you feel comfortable doing a rectal on him would be to don a latex glove, lubricate it with K/Y or Vaseline and gently insert your index finger into his anal opening. If you encounter really hard stool, let me know and I can provide over the counter treatment options for you. By the way, you'll probably want someone helping you since he may find this procedure somewhat uncomfortable.
Other possible causes for his behavior, though, include the following:
1. Compression of the spine by a intervertebral disc is a really common problem in this breed as you know. Even mild compression could be uncomfortable. While a thorough physical exam or an x-ray may be suggestive, sometimes it takes additional testing such as an MRI to confirm.
2. As strange as it sounds, I have seen some dogs with anal glands behave as you describe. If you are not familiar with these glands, this LINK discusses them in detail.
Some dogs are extremely bothered when these glands fill up which causes pressure on their bodies and will continue to do so until they are emptied. Although a groomer can provide this service for you, they usually attempt to empty the glands externally. The better method is done rectally which is how a vet tech or your vet would empty them.
Many of these dogs are reluctant to jump, they hold their bodies in an awkward way (trying to minimize pressure on their anal area), and sometimes will hold their tails down.
Many small dogs find anal gland pressure to be quite uncomfortable which might explain his panting and vocalization.
If he's not vomiting nor taking any non-steroidal anti-inflammatory medication, then Aspirin can be given at a dose of 10 mgs per pound of body weight, twice a day, with food to avoid stomach upset.
The anti-inflammatory as well as anti-pain properties of this drug may be helpful in this situation regardless of the underlying cause (except if he's constipated).
My only hesitation would be that it might interfere with what your vet would want to prescribe if he has to be seen and if #1 above is deemed to be the problem.
I hope this helps but keep me posted if you perform a rectal on him and encounter really hard feces in his colon. Deb