It depends on the brand. Bosch has a line that requires no electricity at all.
http://www.cpotanklesswaterheaters....,pd.html?start=1&cgid=bosch-tankless-aquastar
I would look and see if it is adjusted correctly. I put an tanklless electric one in my mothers house when I rebuilt it and it had a very fast response time. It took maybe 5-10 seconds for hot water to come out of the farthest tap away from the unit which was faster than the previous water heater.
Lag on a tankless comes from two sources.
The water in the pipes between the unit and point of use. - There is not much you can do about that, aside from moving the unit, or purchasing point of use units.
The amount of water that flows through the unit before the heating element gets fired up. You can adjust that, and different units do have different response rates. You can also mitigate it a bit by not opening the hot faucet full blast initially.
My idea solution is to take out our existing gas fired boiler (hydronic heat) and replace it with a condensing unit and run a priority zone off of that into a hot water holding tank. The payback is not really there, the current boiler is 80% efficent, so to go to a +/- 93% efficent unit would not pay that well. There are other issues to consider though. I have a split level with no basement. My boiler and water heater on in the middle of the first floor of the house - in the laundry room. With a gas furnace, gas clothes dryer, and gas water heater I worry about make-up air. There is a also a fireplace on this floor, adding to the combustion mix. A condensing unit would solve the problem of make-up air nicely and I could route the exhaust and supply up the chimney. However if I go with a seperate tankless unit and do not replace the boiler, then I need to think about where to route the exhaust and intake. Unfortunately there are no other good options from where the untility room is currently located. I would have no trouble tying a traditional gas water heater into the existing chimeny. I just put a liner in, and when I bought the liner I purposely made sure that what I was buying could handle the combined BTu's of both my existing gas boiler and a new gas water heater.
I would also love a condensing unit and a small tank because that would free up a lot of space in the laundry room, and I could then fit a water softner in there (yeah, the city water service also comes up through the middle of the slab - I wonder who's bright idea that was)
Clearly what I need to do is win the lottery and then I can rip it all out and start fresh.
-dave