There are two parts to this, and one is more troublesome than the other. The simpler part is that the Fed can influence changes in NGDP--the money value of output, or "demand"--more directly than it can influence inflation. The Fed has no control over the way a change in demand divides between higher real output and higher prices. Therefore, it should not be held accountable for the split. But it can and should be held accountable for how the combination of the two--NGDP--evolves.
The trickier question is whether to express the target as an annual rate of change or as a medium-term path. This choice, by the way, has to be made whether you target NGDP or prices. Setting the target as a path aims in effect to claw back some of the fall in demand--or deviation in the track of prices, as the case may be--which happens during a recession. The Fed strives to get NGDP back to where it would have been if the recession had never happened.
The key thing is that with a target expressed as a path, NGDP would need to grow faster than normal during a period of catch-up following a recession. Setting the target as an annual growth rate, with no allowance for the shortfall just experienced, would fold the recession-induced decline in NGDP into a new baseline.
Romer argues for a target path. I agree, because the policy should allow for some catch-up. However, advocates have to admit that this complicates things. A deep and long recession may undermine the economy's long-term capacity. Getting back on the pre-recession track may be difficult or even impossible--and trying to do so regardless would be inflationary.
In practice, therefore, discretion re-enters. The target path will sometimes need adjustment. This makes it harder for the Fed to explain what it is up to, and lessens the presentation-and-accountability benefits of switching to an NGDP regime. It's another way of saying: however you do it, monetary policy cannot be mechanical. But it can be improved, and a switch to NGDP would help. That point stands.