It runs in a split second for me. Are there preexisting assignments to some variables?
In[669]:= Solve[{vccp ==
ReplaceAll[{vc1n1 -> vc1p, vc3n1 -> vc3p, voutn1 -> voutp}][
vcc[n]],
vc2p == ReplaceAll[{vc1n1 -> vc1p, vc3n1 -> vc3p, voutn1 -> voutp}][
vc2[n]],
vc3p == ReplaceAll[{vc1n1 -> vc1p, vc3n1 -> vc3p, voutn1 -> voutp}][
vc3[n]],
vc1p == ReplaceAll[{vc1n1 -> vc1p, vc3n1 -> vc3p, voutn1 -> voutp}][
vc1[n]],
voutp == ReplaceAll[{vc1n1 -> vc1p, vc3n1 -> vc3p,
voutn1 -> voutp}][vout[n]]}, {vccp, vc2p, vc3p, vc1p, voutp}]
(* Out[669]= {{vccp -> vcc[n], vc2p -> vc2[n], vc3p -> vc3[n],
vc1p -> vc1[n], voutp -> vout[n]}} *)