There are so many serious problems with the grey goo worry I don't know where to start:
Energy:
These minature robots need a power source. I assume we all agree anything larger than 1mm^3 isn't a threat, because we can just shotgun the bastards, even assuming some amazing software and hardware which allows replication from ores (which is what they'd need to do). Anything smaller would need to power itself. Any energy source that can be used (which excludes nuclear and fusion for obvious reasons, no matter how advanced the tech.) would result in a life of around 1 minute. This isn't practical, so they'd need to have their power beamed to them somehow. If this is the case, then it'd be childsplay to stop or interfere with this beam, hence no threat.
Replication:
To convert scrap into material for manufacture requires a large amount of energy (see above), and also a huge amount of equipment. Think of a blast furnace or an aluminium plant. Little robots could not do it like that. So, they'd need nanomanufacture. This has been shown to be hugely energy inefficient compared to traditional methods, even using pure theory with 100% efficiency. This is because you'd need to assemble such small pieces (nano-scale) rather than, say, cast or forge a component.
Computational ability:
Little robots would not be able to run a program of any reasonable length with any reasonable speed. You'd need distributed computing, ie a lot of them linking up to do their calculations. To do anything reasonably intelligent they'd either need to be very large (in which case some battle against them could be easily won), or have their instructions sent to them. Luckily we don't need wireless data transmission to survive, so we can just flood the area where they are a threat with EM noise, which thankfully is exceptionally easy to create, even at massive volumes.
So, in a nutshell, there is no threat whatsoever from some sort of nano-bot.
