This is appears to be a common problem with the Bissel Canister Cleaners with some age on them. I had to fix my model 1660, with the same symptoms.
The pump motor assembly likely needs replaced. They sell for around $25.00 USD + S & H on eBay. (you didn't say which model you had, but, they all seem to be around this amount.) I don't know what the cost direct from Bissell is, or if they are even available. They do have a toll free number if you wanted to check. Bissell Customer Service: (800) 237-7691
sfsjet, December 2006
