Economics has this thing called "the multiplier effect." When an income is lost, it represents less money in the economy. So, if a federal worker loses their job, they have cash to buy groceries. That means the supermarket makes less profit. So, the super market has to let some its workers go. It's a chain/ripple effect, and it doesn't matter which sector of the economy the paycheck originally came from.
The government likes to spend money on items that the public doesn't need. When any layoffs happen, it does affect the economy. People are collecting unemployment, and not spending money to stimulate the economy. People are being more conservative due to higher prices and less income. If I balanced my check book the way the government balances their's, I would be in prison for the rest of my life.
The economy is driven by the private sector, not the government. The government cuts have very little to do with the overall economy. The majority of jobs are in the private sector and private companies are not hiring. The current administration’s view on taxes and healthcare are making private companies more weary of hiring more people. Companies know that under the new healthcare requirements it will be more expensive to employ each additional employee. The economy is unlikely to improve while there is still so much concern over the effects of the healthcare law.
Unless you work for a statistics company, how can you really tell? There are so many jobs lost each year that trying to answer this is almost impossible. The government is the biggest waster of money and if you have some sort of political affiliation you get a job. No fuss, no muss! You're in.