Consequences of sub-exponential proofs/algorithms for SAT

Would there be any major consequences if SAT had at most subexponential unsat proofs or even more strongly, SAT had subexponential-time algorithms?

• It would disprove the exponential time hypothesis which has various consequences (covered in the wikipedia article). – Artem Kaznatcheev Dec 2 '11 at 3:20
• @ArtemKaznatcheev comment -> answer ? – Suresh Venkat Dec 2 '11 at 3:34
• @SureshVenkat feels kind of awkward to give an answer when Ryan Williams can provide a much better one. I gave one for now, but I hope Ryan and others pitch in with something cooler. – Artem Kaznatcheev Dec 2 '11 at 4:05
• If the answer is correct, it doesn't matter who gives it :) – Suresh Venkat Dec 2 '11 at 6:00
• Sorry Artem, my answer wouldn't be much cooler than yours... I guess one thing to add would be that ETH is false implies new superlinear circuit lower bounds (same paper). – Ryan Williams Dec 3 '11 at 3:39

For fun consequences: if you showed that circuit SAT over AND,OR,NOT with $$n$$ variables and $$poly(n)$$ circuit gates can be solved faster than the trivial $$2^n poly(n)$$ approach, then by Ryan Williams' paper you show that $$NEXP \not\subseteq P/poly$$.