Look: this isn't complicated. Nobody can find a job, because nobody in the private sector is hiring, and the public sector is laying people off. The public sector part is straightforward: budget cuts mean layoffs. The private sector is only slightly more complicated.
As each company is deciding whether to hire or not, they ask the following question: "am I better off with my money in the bank, or invested in the economy, paying somebody to make a product that I can sell?" Right now, inflation makes cash lose about 1% per year of value, so any investment that does better than that is a good deal, but obviously that's not enough to get companies hiring. To fix this, we either need to make more investments look like they'll pay off (ie, improve demand), or make "safe" assets lose money more rapidly.
So: The government can either buy stuff to fix the demand directly, or create a bit more inflation. Take your pick. Either one will work, but shy of that the economy is going to suck for a really long time. It's just that simple.
Republicans keep talking about exploding spending under Obama. So, here we have public sector spending under the spendthrift Obama vs under republican Demi-God Reagan, shamelessly lifted from Paul Krugman
In '82, the government increased spending by 10% over the 4 years after the recession, but in the last 4 years, government spending has fallen by 3% or so. Unsurprisingly, budget cuts mean laying people off, which has not done any favors for the unemployment rate.