Not quite as simple as your statement reads.
Out of the the Government employees effected only a portion continue to work without pay, these employees will only receive their back pay if the Congress approves the payment.
The other large number of Government employees effected are on furlough without pay, they are not reporting to work and will not be paid for their time off, so yeah, a little more then one dime.
If this shutdown continues to a point these working employees do not receive a paycheck, they still have bills to pay, many live paycheck to paycheck. This disruption can cause some issues even though it is likely they will eventually receive their pay. The furloughed workers are not so lucky.
I believe your son is attending the Citadel, remember one day soon he'll be a "gubbamint" employee.