Analyzing recent experimental results [ Reulet et al. Phys. Rev. Lett. 85 2829 (2000); Izmalkov et al. Europhys. Lett. 65 844 (2004)], we find strikingly similar behaviors between two very different systems: three-junction superconducting qubits and suspended carbon nanotubes. When these different systems are ac-driven near their resonances, the resonance single-peak, observed at weak driving amplitudes, splits into two subpeaks for strong driving amplitudes. We describe this unusual behavior by considering quantum tunneling in a double well potential. Inspired by these experiments, we propose a mechanical qubit based on buckling nanoscale bars (nanobars)—a nanoelectromechanical system so small as to be quantum coherent. We consider how this nanomechanical qubit can be manipulated. A comparison between nanobars and superconducting qubits suggests several future experiments on quantum electromechanics.