A multi-target attack on 128-bit ECDSA private keys
One $n$-bit ECDSA private key can be found from the public key with about $2^{n/2+1}$ group operations, by Pollard's rho, which is relatively easily distributed. Nothing more costly is worth consideration. For $n=128$, this is $2^{65}$ field operations and would be feasible with a large effort. This is why people use at least $\approx160$-bit ECDSA, and more like $256$-bit ECDSA or more nowadays.
It's a more interesting problem to determine if a multi-target attack can take sizably less time. I do not immediately see that it does.


How long would it take for a computer to perform $2^{64}$ ECDSA operations?

That depends a lot on:

The computer. This one is millions times faster than most others.
What's an operation. A full ECDSA signature at $n$-bit costs in the order of $n$ times more than a group operation, wich costs several field operations.
The $n$ parameter. For medium values, doubling it multiplies the cost of a field operation by like 3, of a full ECDSA signature by like 6.
The curve used. Binary curves allow faster implementation and attacks.
Competence of the attacker, which matters immensely.

Ultra rough estimate with my PC for $2^{65}$ group operations: $2^{31}\,\text{Hz}$, $2^3\,$cores, $2^7\,$cycles per field operation, we are talking $2^{65-31-3+7}=2^{38}\,s$, that's many centuries. We need too many PCs and too much energy.
Therefore the attack for $n=128$ has no practical interest, is feasible only at sizable cost, and it's better to run it as a mind or small-scale experiment.