War with Pak: Yes
There is no way Pakistan govt will help finding perpetrators of any terrorist attacks that have happened in India over the past, forget about current Mumbai attacks. This is shown in their blatant act of ignorance that any terrorist activity even does exist in Pakistan at all. Similarity can defined for Pakistan govt with Taliban which did not take any action against Al Qaeda, and now Pak is reluctant to recognise LeT (and group). Pakistan's behavior in this respect is also criminal, giving refuse to other criminals. It is Pakistan's compulsion or urge, we cannot tell. How to pressurize Pakistan is question which is answered by only taking unilateral military action.
We are left with only military action because over the past, any bilateral or multilateral talks involving India and Pakistan, have been failed utterly in achieving the objective. Though one should not be cynical that if talk has been failed in the past, it is bound to fail again. But going with conditions in Pakistan and attitude of its govt, it is safe to assume.
The other way would have been multilateral pressure on Pakistan with the support of USA(may be Israel also). But here again the glitch is at this point of time, favoring India over Pakistan is not in strategic interests of USA. USA would not want to jeopardize its fight with Taliban on Eastern front of Pakistan, which is its high priority and in which it has already invested.
All India is left with, is unilateral action(not talk) on Pakistan which transforms to war.
War with Pak: No
The solution is not so easy. Lets say we go to war with Pakistan.
First of all that is really not direct solution to India's problem. 'War' means war with Pakistan govt which is in fact supporter of terrorists, not the actual culprit which happens to be LeT and Company Inc.
Secondly there is the mess of Taliban. If there is war between Pakistan and India then Pakistan finds itself in pieces. It will be highly unstable because of war from two fronts - Eastern(India) and Western(Taliban). Now again, unstable Pakistan is highly undesirable for India. India may win one war, but will have to face another war.
There maybe a arguments that Taliban will support Pakistan. Really? The given war will be only platform for Taliban to gain solid stand in Pakistan. After Pakistan goes bust, Taliban will rule the left-overs. Taliban is no mere terrorist group, it has a monumental army gathered(80,000 read somewhere).
On top of that, If India goes to war with Pakistan then it will jeopardize its strategic relations with USA because for USA Pakistan is a crucial ally in fight with terrorism. And in this situation when India is vulnerable from three fronts - Pakistan(west), China(Northern border) and internal threats(like naxalism), it will be a blunder to not have USA as an ally. Because at this point of time, on international front only USA is strong ally for India.
The Question
What should be India's response, as foreign strategy, to Mumbai Terror attacks?
still remain unanswered.