The recent paper on Diffie-Hellman "precomputation" estimates a cost of 45-million core-years. Of course, the NSA wouldn't buy so many computers to do the work, but would instead build ASICs to do the work. The most natural analogy is how Bitcoin works. Bitcoin hashes were originally computed on CPU cores, then moved to graphics co-processors, then FPGAs, then finally ASICs.
The current hashrate of Bitcoin 460,451,594,000 megahashes/second. An Intel x86 core computes about 3-megahashes/second, or 153,483,864,667 CPU cores. Divided this by 45-million core-years for precomputing 1024bit DH, and you get 3410 DH precomputations per year. Thus, we get the following result:
The ASIC power in the current Bitcoin network could do all the necessary precomputations for a Diffie-Hellman 1024 bit pair with 154 minutes worth of work. Or, the precomputation effort is roughly equal to 15 bitcoin blocks, at the current rate.(Update: I did some math wrong, it's 154 minutes not 23 minutes)
Another way of comparing is by using the website "keylength.com", which places the equivalent effort of cracking 1024 DH with 72 to 80 bits of symmetric crypto. At the current Bitcoin rate, 72 bits of crypto comes out to 15 bitcoin blocks, matching the estimate above. (I assume precomputation is roughly the same amount of work as computing 1024 DH).