You ask a few different, though not unrelated, questions.
Everywhere you turn today, you hear
people talk about how much they need
to save or how important it is to find
a good deal on things "in this
economy". They use phrases like "now
more than ever" and "in these
uncertain times". It seems to be a lot
of doom and gloom.
Some of this is marketing spiel. You may notice that when the economy goes south the number of ads for the cheaper alternatives goes north. (e.g. hair clippers, discount grocery stores, discount just about anything) Truth is, we should always be looking for ways to save money on goods and services we purchase. The question is, what is acceptable to you for your desired lifestyle. (And, is that desired lifestyle reasonable for your income, age and personal situation.) Generally speaking, the harder times are the more we find discounted/cheaper alternatives acceptable.
Is there really a good reason that
people should be saving more than
spending right now?
How much you are putting away is a personal matter. I can still remember my dad griping whenever he couldn't save half of his paycheck. That said, putting away half your paycheck may lead to a rather austere lifestyle. This, of course, depends on the size of your paycheck and your desired lifestyle. You could be raking it, living simply and potentially put away more than half your income with relative ease.
If you have a stable job, and a decent cash reserve, is it anymore "dangerous" to make a large purchase now than it was seven years ago?
Who knows? Honestly, no one. Predicting the future is a fool's errand. (If you are interested in reading more on this view point, I suggest The Black Swan.)
You mention the correct approach in this question. Ensure that you have liquid assets (cash or cash equivalents, i.e. money that you can draw on immediately and isn't credit) which covers at least 3-6 months of your necessary expenses (rent/mortgage, bills, car payments, food). (There is no reason that you couldn't try to increase this to 1 year, especially "in this economy.") You should also strive to have money available for emergencies that don't necessarily include loss of income. Of course, make sure you're putting away for retirement, as appropriate for your retirement goals. After that should come discretionary items, including investing, entertainment, the large purchase you mentioned, etc.
You should never use money that you may need immediately (5-10 years) for investing. This doesn't necessarily include the large purchase you are contemplating. For example, if you are considering purchasing a home, the down-payment may be one of the items for which you need money in the "immediate" future.
Is it really only because of unemployment numbers?
This is probably the big one that is the focus of everyone's attention. That said, the human attention span is limited. We have a natural need to simplify things. This is one of the reasons that we tend to focus on a few, hopefully important, things. However, the unemployment numbers are not that the only thing of concern. Credit is still pretty hard to come by these days. The overall economy is still hurting, even if we are technically no longer in a recession. There are also concerns about U.S. government borrowing, consumer spending, recent trucking numbers, etc. (It may not be obvious, but trucking is used as a barometer of economic activity. If there aren't as many trucks carting goods across the country, it probably means that there is less economic activity.) The headline number these days is unemployment, as most census workers have now been returned to the pool.
To answer the overall question, we should always be saving money, in good times or in bad. Be that by squeezing more value out of our purchases or by putting some money away. We should always try to reduce our risks, by having an emergency "cash" cushion. We should always be saving for retirement. Truth be told, it is probably more important to put money away in good times, before the hardships hit.