for those of you(like me) wondering where this apparently spooky constant is coming from, it is a bitstring of the coefficients of the lexically first irreducible polynomial of degree b with the minimum possible number of non-zero terms, where b is the block size(in bits) of the underlying block cipher with which CMAC is instantiated. So, nothing up the sleeve here.
Investigating further, general-case CMAC involves generating a K1 and a K2, which afaict just need to be arbitrarily different from each other. So why not something even simpler, like "xor with 1"?
The input here is highly restricted so there's no point to it.
The answer is that we're treating this as a Galois field/finite field of order 2^128 with the reducing polynomial (2^128 + 0b10000111).
Under that framework, the left shift and possible XOR implement multiplication by 2. (An example of general multiplication here: https://en.wikipedia.org/wiki/Finite_field_arithmetic#Progra...)