Is this normal?
Yes, it is. Sinew and other connective tissues (silverskin/fascia, ligaments) are very tough stuff; you need to remove as much as possible by hand before grinding.
Sinew and ligaments are strong, whitish strands or "cables" connecting bones to muscles and to other bones, respectively. They'll be in the same place on every piece of a particular cut of meat: a poultry drumstick has an easily-identifiable piece of sinew -- actually the "Achilles' tendon" -- heading from the fleshy part to the exposed end of the bone.
Silverskin is a connective boundary between muscles. It's a thin, clingy, and annoying sheet, translucent silvery white, that you will find on the surface, and defining the divisions of, various cuts of meat. It might make it through the grinder if your blade is nice and sharp and the piece isn't too big, but it's best to take it off (your teeth can't deal with it much better than the grinder can). You'll need a thin, sharp, narrow blade for this: a filet/boning knife, sometimes a good paring kife.
Essentially, anything that's not fat or muscle needs to be taken out before the meat goes into the grinder.
Chicken thighs have a lot of connective tissue. Some of it is hidden inside the muscle segments on the underside of the thigh; make sure you cut those open.
Depending on the particular piece of meat you have, you may end up with what seem like extremely small bits after this process. Even a nice pork shoulder can result in 1/4" or thinner pieces after the internal connective tissue is removed. This won't have any real effect on the grinding process; the only thing to watch out for is thorough and even mixing if you end up with many different sizes and are marinating/curing the meat before grinding.
You can grind without removing all the tissue (it gets frustrating sometimes), but you'll have to be prepared to stop the grinder and clean the blade and plate frequently -- the instant you notice that the meat is not coming out of the plate in clean, cohesive, and separate lines. If you see any signs of smearing or over-grinding (the grind will start to be too fine and become pink as the fat and meat combine), stop and clear the blade. Otherwise, the mixture won't emulsify properly, the fat will melt out when you cook it, and the sausage will be dry.
Does my blade need sharpening already?
It may very well, but this still won't help with sinew and ligaments.
You should treat your grinder blade the same way you treat your kitchen knives -- maintain its edge, rather than waiting for it to become completely dull. I'd say that I put my blade onto a sharpening stone every 50 lbs. or so. The nice thing is that it's extremely easy -- you are grinding all the arms of the blade at the same angle: flat. The plate also needs to be maintained by grinding the surface where it meets the blade (the edges of the holes should be sharp), but I'd say that this can be done much less freqently. The blade and the plate can both be maintained quite successfully and easily with a piece of fine (800 grit) wet-dry sandpaper slapped on a table.
Best Answer
A probable answer is that maybe it wasn't intended to be firm at all.
There are different types of liverwurst in Germany. The most commonly sold one is indeed firm, but from its texture, I'd guess that it has gelatin added. It is more rubbery than the naturaly gelled meats I've eaten. But there is no guarantee that your recipe was intended for this kind.
Another common type is the spreadable liverwurst. It is a creamy mass which is intended to be spread on bread similar to cream cheese. If you want to make this kind, the meat grinder is probably only good for the first pass. I'd make sure to puree it really fine, a blender is probably better. (Unless you specifically want to make the chunky type).
I am not too sure that pork shoulder is such a good choice, probably the fat wasn't enough. The most popular recipes on chefkoch.de (a site similar in quality and popularity to allrecipes) call for pork belly, the part which is made into bacon. Some of them also say to add
speck, which is the non-rendered subcutaneous layer of fat of the pig. It also tends to come from the belly (sometimes from the back), but has less or no meat attached. Many specify that the meat gets cooked first, then ground. The raw liver gets ground separately (after removing fascia and the ducts). Then everything is mixed, pureed (or regrinded for chunky). Then it is filled (some use natural casing, most fill it into jars, nowhere was muslin mentioned) and sterilized. I found some variance among the methods, but as I haven't tried any of them, I can't tell you which works best. I didn't find a recipe which was explicitly for firm liverwurst, but many of them explicitly mentioned spreadable liverwurst.I also found some discussion on the proper ratio. This varies (depending on taste) between the liver being 20% to 33% of the whole mass. A higher ratio seems to cause both dryness and bitter taste.
This is probably helpful if you can live with spreadable wurst. If you insist on the firm kind, you may have to experiment with gelatine, because I couldn't find any homemade recipes for that.
Edit: some more research suggests that the denaturing proteins in the liver are enough to bind the leberwurst to be firm, and adding some of the fatty water in which the meat cooked makes it spreadable. The one who wrote it seemed to have some authority on making sausages (at least he made lots of posts and the others didn't disagree with any of them). Again, this isn't my opinion, just a translated summary.