Answer
One way a government deficit hurts a future worker is that, when the government debts come due, the workers must decide to either have higher taxes and and less government spending (to make other resources available to pay off the debt) or push the government into even more debt (and roll over the debt).
Work Step by Step
Another way a government deficit hurts a future worker is that a deficit means that public saving is negative. This would also decrease private saving. The decreased saving increases the real interest rate and cuts the level of investment in the economy. In turn, the decreased investment level will lead to smaller levels of capital. The lower capital levels lead to lower labor production levels, lower real wages, and lower levels of GDP.