This is from Dr. Bill's link:

Scouse. Even the O.E.D. says only "slang". I know you'll better that.

Us? Do better than the OED? Oh, the hubris! How could mere mortals such as we ever presume to improve upon that august arbiter of etymology? How? Like this...

We assume that by scouse you mean Liverpudlian, that is someone (or something) from Liverpool. Scouse is also a kind of stew, more properly known as lobscouse. This latter word is of obscure origin but is synonymous with loblolly. It is supposed that the lob part of the words is the same as the dialect word lob meaning "to bubble noisily while boiling" which was applied especially to porridge. The lolly in loblolly seems to be an obsolete Devonshire word for "broth, soup, or other food which is boiled in a pot". The earliest recorded use of scouse (the soup) may well be in "Two Years Before the Mast" by R. H. Dana (1840) - "The cook had just made for us a mess of hot scouse".

Lobscouse seems to have been popular with (or at least endured by) sailors and lobscouser was slang for a seaman. It is no surprise, therefore, that scouse should become associated with Liverpool, one of the world's busiest seaports. So, how long has scouse meant Liverpudlian? Well, slang words tend to have considerable currency before they are ever committed to print but the earliest use to come to our attention was in a 1945 court case when a judge interrupted testimony to ask the meaning of the words Geordie and scouse. He was informed that they referred to inhabitants of Newcastle-upon-Tyne and Liverpool respectively.