This letter studies the application of backscatter communications (BackCom) assisted non-orthogonal multiple access (BAC-NOMA) to the envisioned sixth-generation (6G) ultra-massive machine type communications (umMTC). In particular, the proposed BAC-NOMA transmission scheme can realize simultaneous energy and spectrum cooperation between uplink and downlink users, which is important to support massive connectivity and stringent energy constraints in umMTC. Furthermore, a resource allocation problem for maximizing the uplink throughput and suppressing the interference between downlink and uplink transmission is formulated as an optimization problem and the corresponding optimal resource allocation policy is obtained. Computer simulations are provided to demonstrate the superior performance of BAC-NOMA.