Why couldn't the TARDIS power both Tesla's Wardenclyffe Tower and its force field at the same time?

Instantaneous vs Sustained energy

The Doctor in the episode itself telling us the TARDIS doesn't have the power for both as fact is all we have to go on. So either we use other considerations to determine she's wrong or lying, or we try to find considerations that provide a rationale for her statement. There's no way to know for certain, but there is at least a plausible explanation in considering the TARDIS' energy output at any given moment may be far below its total sustained output over long periods of time, which is true of power sources in reality as well.

While the TARDIS does have the Eye of Harmony as a power source, that doesn't necessarily mean it can utilize all that energy all at once. As an example, a lightning bolt contains 10 billions watts of electric power, which is roughly equivalent to what the Palo Verde nuclear power plant in Arizona puts out in 2.5 hours. But you couldn't just pull all that energy out of the power plant instantaneously, nor could you simply charge 10 billion watts worth of batteries with a lightning bolt. The load has to be drawn out over time. As a general rule of thumb, capacitors are needed for large bursts of instantaneous energy, after which they have a recharge time to regain their potential.

So for all the power the TARDIS has at its disposal, it's entirely plausible that in order to output enough energy to charge the tower with spacecraft destruction-worthy amounts of instantaneous electric potential, the TARDIS shields would be drained enough to no longer be an effective defense until the capacitors could be recharged. Considering the we've never seen the TARDIS to have any apparent offensive capabilities that would require such an instantaneous drain of its power reserves, it just may not have been designed to need to support that sort of power utilization.