Hello, I'm sorry to hear about Rudy. This is very concerning.
Dogs that are painful may hesitate jumping or climbing stairs and display the sort of behavior he is, either because it hurts to do the activity or because they feel weaker than usual. We need to figure out whether he is too painful to get up to move around or whether he has truly lost the ability to do so.
If you pinch his toes can he feel that?
Is he able to consciously control his urine and stool? Or does he seem to be incontinent?
Unfortunately Dachshunds as a breed are prone to a problem with their intervertebral discs, which are the spongy cushions between the individual vertebrae in their back and neck. These spongy discs can move or rupture and place pressure upon the spinal cord which can lead to pain, and in severe cases paralysis.
Radiographs can sometimes be diagnostic but often early on in the disease process, because the discs are soft tissue not bone, everything will look normal. An MRI is the best way of diagnosing disc disease.
If the dog is painful but has no evidence of paralysis we can try strict rest, anti-inflammatories and pain medications for several weeks to allow healing.
If there is evidence or weakness or paralysis then surgery by a board certified veterinary neurologist, as soon as possible, is indicated.
Ideally he needs to see a veterinarian, and if he truly cannot feel his rear legs this should be on an emergency basis tonight. If this is indeed a disc problem the veterinarian can prescribe a steroid or nonsteroidal anti-inflammatory to relieve pressure on his spinal cord and nerve roots, as well as something for pain too, such as Tramadol. And if he is having painful muscle spasms then a muscle relaxant such as methocarbamol as well. If he has lost all sensation they will likely recommend referral for surgery to try to relieve pressure on his spinal cord.
He should be closely confined starting now. No access to stairs. 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 be carried out and 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. You will 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 back, but is no guarantee that he won't have another episode. Once a dog has one bad disc the likelihood of another 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
There are other less common causes of back pain or weakness such as infections, tumors of the vertebrae or the spinal cord itself or fibrocartilagenous emboli but far and away disc disease is the most common cause of rear leg weakness and pain in dogs.
Please let me know if you have any further questions.