What is the frequency of the signal you are trying to remove?
Depending upon the frequency, you may be able to minimize high frequency spikes without significantly affecting the low frequency phase shift by using a slew-rate limit filter, such as a low frequency op amp with a slow slew-rate. The op amp will not be able to slew to the peak of the high frequency spikes but will readily pass the 60Hz signal. You still will likely need some low frequency roll-off on the op amp, but just make the low-pass frequency high enough to avoid significant phase-shift at 60Hz.
Typically very low power op amps, such as the **broken link removed**, have low slew rates and should be good candidates for this application. Generally the lower the power, the slower the slew rate. EDIT: An even lower slew-rate unit, for example, is the LTC1542.
Usually you want a high slew-rate op amp for better high frequency performance, but here you want just the opposite.