Due to the tensions between USA and Russia over Crimea, and the fact that Russia is the second biggest nuclear power, is the US considering resuming the Brilliant Pebbles project in subsequent years?
It seems unlikely that missile defense, especially systems that will require significant expenditure on research, testing, and deployment, will be pursued.
First, there's little public noise over dramatic moves in the missile defense arena. There is not a strong sense among even conservatives that missile defense is truly a critical move. The nuclear threat has receded somewhat from public consciousness, with current fears focusing more on terrorism and perhaps brief border conflicts. Without pushes from foreign policy commentators, cries from politicians, or grumbles of interest from the public, I don't think a significant new missile defense technology is likely to be started or deployed any time soon.
Second, it's not clear that missile defense would be that useful in this situation. Leaving aside the questions of efficacy, which have always been a prominent part of the missile defense debate, is the question of whether the US would change its behavior if it did not fear nuclear retaliation.
Missile defense itself cannot stop Russian unmarked troops from surrounding Ukrainian airports; unless the US and the West take martial action against Russia, the shield is not relevant. It seems unlikely the US would nuke Russia, even just a few tactical nukes, over this invasion which likely has some level of support from a significant number of Crimeans (ignoring the sham referendum) - and it's not clear whom to nuke (civilians in Moscow? Crimea naval base? civilian casualties seem inevitable and world opinion would be irretrievably hostile). So then you have the US engaging in maybe an air war a la Kosovo/Belgrade 1999 - something like drones, bombers, conventional cruise missiles - blowing up huge swaths of the Crimea to save it? Also unlikely.
Until the US is willing to make nuclear strikes or engage in conventional warfare against a major secondary power (freed of the fear of conflict nuclearization), a missile shield is not a very meaningful change to the situation. So why bother with an expensive shield if it doesn't significantly change your decision-making calculus?
Third, the efficacy of almost any new missile system is controversial. I include by reference here the many claims against possible weakness of missile defense technology. I don't have the expertise to parse the various claims, so I'm not making a conclusion. But the mere fact that these claims are made by so many people and taken as credible by so many others is enough to present a large hurdle to a new missile defense technology.
Fourth, the cost will be significant. As I said above, this system will require significant investment to make operational. The financial crisis may be receding in our memories, but budget deficits, debt ceiling showdowns, and entitlement crises are not likely to all disappear at once. The demographic crisis is only worsening. The capacity of the US the undertake expensive projects that are of dubious or arguable value is relatively low. It would also face a reasonably high level of opposition even in conservative ranks, given the prominence of spending hawks in the House and Senate.
Fifth, it seems likely to be seen as a provocation. Both Russia and the rest of the world may interpret this move as an aggressive one intended to pressure and isolate Russia. The implicit goal is to allow the US to threaten Russia (and China and the rest of the world) with nuclear annihilation without fearing the same in response. That's going to cause consternation in a lot of quarters, including within the West. There are reasonable fears that it might encourage arms competition or at least derail good faith efforts at nonproliferation. It could also cause non-shielded states to engage in more covert methods, such as espionage and terrorism, for which a shield is less effective and a nuclear response would be unjustified. In other words, it may actually make the world less safe rather than more.
So no, I don't think the US government is likely to reconsider space-based missile defense any time soon. The technology has shifted, so maybe it's more achievable than ever. And in principle, the idea of rendering nuclear weapons obsolete is a very powerful one. But I don't think this Crimean invasion is going to trigger a major shift towards space ABM technology.