A soliton microcomb requires increasing pump power as its optical bandwidth is broadened. Resonant pumping through an auxiliary microresonator can reduce the power required to sustain a soliton, but simultaneously increases the power required for soliton formation. We show that this competition leads to optimal inter-resonator coupling, and the predicted minimum input pump power scales as the two-thirds power of the comb bandwidth, in contrast to the quadratic scaling under direct pumping. Experiments support the opposing power trends, providing a design rule for power-efficient, ultra-broadband soliton microcombs.