A Couple of Things I'm Wondering About

I've refrained from commenting on political stuff, but after the president's speech the other day about the debt ceiling "crisis" I'm wondering about some things.

The president said that even if we cut spending, we have to raise taxes anyway. My question is this:

I'm using small numbers to illustrate, 'cause trillions are hard to write and understand.

If we're taking in say $1,000 in taxes, fees and other stuff

And we're spending, say $1,500 for everything we spend money on (I don't think that SS and Medicaid are in the regular budget, allegedly they have their own income streams)

That leaves us overspending by $500 (and we wouldn't be in debt if we weren't overspending)

Now the republicans want to cut spending, so if we were to cut spending by say, $800

that would leave us with $300 dollars that's not getting spent, in effect it's helping to bring down the deficit. 
Why do we absolutely have to raise taxes? Why not encourage businesses and people with extra cash to invest in the economy?
And what about the money that some agencies don't spend? Why isn't that money put back into the pot and their budget lowered to be a realistic one?
Just wondering.

Something else, I'm really wondering.
Are the publishers and editors at Newsweek really so lacking in taste they they had to run a "Diana at 50" cover and story?
Is there nothing else newsworthy enough to focus on?
When did Newsweek turn into the National Enquirer?