There is no direct causality link between unemployment and the deficit. Unemployment is the result of a disequilibrium between too few employers and too many employees. This disequilibrium could easily be resolved by lowering wages and allowing wages to fluctuate according to the demand for labor. Instead, we impose a minimum wage and subsidize those who do not work, which greatly exacerbates the problem.
As for the deficit, any time government spends money it will result in more public sector (and some private sector) employment. The deficit could have the effect of temporarily boosting employment by increasing the number of government employees. On the other hand, companies that invest in a country's economy see the massive deficits and understand that this means greater taxation-- or even possible confiscation of their businesses -- in the future, so they become hesitant to invest private capital in the economy. This is happening at present, as there is an estimated $3.5 trillion in unused capital sitting on the sidelines (ie, being hoarded) in the USA. Also, a whole bunch of additional money is finding its way into foreign markets that are more attractive than ours. Of course, this retards employment.
Therefore, over the long term the deficit contributes to greater unemployment and a lethargic private sector. But if there were no deficit and taxes were raised instead, the effects would be much the same. The only difference is that deficit spending means the government borrows what it needs rather than stealing it, and therefore government is paid for by increases in the prices of everything we buy. Inflation is a very regressive tax, but for some reason politicians seem to escape blame for it. Instead, they'll blame greedy business and many people will believe them.
The bottom line is the only way to stabilize our economy (and therefore unemployment) over the long-term is to reduce the size of government to around 20 percent of GDP, which historically seems to be the best balance between the public sector and private sector. In order to do that, the federal government would have to shrink by some 40 percent from its present size.