Of course, one could propose a tax on the rich that improves the situation, but the Democrats don't do that because they are beholden to their rich contributors...

I suppose I was just getting a bit confused by such references as "If you hold a job in the US you pay Federal and State Unemployment tax", which I took to imply that the worker was responsible for the payment on these taxes.

Without spending too much time wandering afield from your basic point regarding differences between German and U.S. benefits and application requirements, I think that it is relevant to some degree "who paid the unemployment taxes".  Very briefly, here's why:

1. Since unemployment taxes are essentially invisible to the worker, it's practically impossible for that worker to gauge whether any benefits they might be unfortunate enough to have to receive are truly at a proper or sufficient amount.
   
2. As the tax burden in the U.S. rests solely with the employer, this has long been a source of resentment among business owners (especially smaller employers) which makes itself an issue at Chamber of Commerce meetings and generally causes those small business owners to ally politically with anti-tax and anti-worker Republicans, who promise to "ease up on regulations that stifle the great engines of job creation in America".
   
3. In Germany, the unemployment tax is 6.5% of gross income -- with a fairly high ceiling -- divided equally between the employer and the worker (this is more than half the figure paid in the U.S. for Social Security taxes).
   
4. Because the tax burden in Germany is shared between worker and employer, there is less incentive for businesses to attempt to minimize the tax rate through legislation or regulation; any movement in that direction would be instantly obvious to the employees as posing a potential direct harm to their benefits.

Sorry for getting a bit carried away here, but these differences in who pays the tax I think does end up having a lot to do with the nature of the benefits in each of the countries.  In the U.S., it is often the high cost of "hidden" taxes on business that is cited as a reason for layoffs.  Since the workers don't see this, they don't realize that a) they have a major stake in the issue, and b) this may be why their benefits are so low.  In Germany, by comparison, it seems like it would be difficult, if not impossible, for each worker to be keenly aware of these things.  With that knowledge, any discussion of potential changes can become precisely the type of hot-button issue in Germany as changes to the Social Security system would be for the U.S.