Interest rates on bonds increase, leading tp increased costs of borrowing. Leads to
a) fall in business investment, which reduces both AD and LRAS (i.e fall in economic growth)
b) structural instability as a result of a)
c) goverment has to increase spending if it wants to maintain the same level of stimulation that government spending has on the economy. If it doesn't, government spending falls in real terms. (thus fall in AD).
d) Due to falling economic growth, unemployment rises. May lead to a vicious cycle of increased welfare payments, which in turn leads to a prolonged deficit, and then more welfare payments.
e) LRAS shifts to the left as said in part a). Thus inflation increases in the longer run.
A few contingent variables
1) The size of this sustained deficit. Is it 1% of GDP, or 20%?
2) The length of the sustained deficit.
3) The global economy. Say, if other economies are also in a period of sustained deficit, then interest rates on bonds may rise simulatenously and investors may not invest elsewhere since it's just as expensive to borrow, leading to no negative impacts on AD.
4) The level of govt spending as a percentage of GDP.
5) Causes of this sustained deficit. Is it in the aftermath of, say, a financial crisis and may be solved when the crisis is over, or is it a more structural issue?