Ok please elaborate what kind of common threat you are facing? I mean what is common?
- China as a rising superpower with nuclear missiles that can reach nearly any country
- Iran and N. Korea which have, or are close to have nuclear weapons and are lead by dictators which openly stated they hatred against the west
- Pakistani nukes in the hands of terrorists
Some of this might not be a current problem for Russia, or India, but could be in future and that's why the US/NATO wants to increase their power by bounding Russia and India to them.
This has more political meaning, than techinical, because Russia and India can develop own missile systems too. But as I said in an other thread recently, the cold war is over and today Russia and India are prefered partners of the west and not threats anymore. The political pressure the NATO can put on Iran, N. Korea, or even Pakistan and China is way stronger, when they have stronger relations to Russia and India.
Wrt Pakistan, one have to look at the current situation now! The war in Afghanistan is going to end soon and the NATO forces will bring back their troops. That automatically means, they don't need Pakistan anymore for the logistical support of their troops. What's left is Pakistans importance in fighting terrorists inside of Pakistan itself, but since the raid on Bin Laden and the possible involvement of Pakistani officials in hiding him, this is getting less important as well.
On the other side, the US pushed India through the nuclear agreement and even pressured some of their NATO allies to get it through. Countries like Japan, Canada, Australia who opposed to sell us nuclear material/techs even for civil use, now are happy to do it, obviously with US backing it. President Obama stated that India could become a permanent UNC member during his visit in India, which the US not even stated about their close allies like Germany, or Japan before. Not to mention that nearly all US weapon systems are on available for India today!
As you can see, the US foreign politic strategy towards Pakistan and India is completelly changing, because their interests is changing as well! It was in their interest to support Pakistan in the past, while it is now more important to support India and that even on a way higher level. This offer to join the missile shield is just the next step and from Pakistans point of view this change obviously is a big problem, while I would say that India should learn from your experience and should be careful and remain indipendent as much as possible. The price we pay is not getting China against us, that's something they did on their own, but to be too dependent on US policies, which is obviously also the reason why Russia will not join them so easily.