Mixing Cipher Lower Bounds
The design you described is very close to Geffe generator - it consists of three LFSRs L1, L2, L3 and the output bit is either the output of L2 or L3 depending on the value of the output bit of L1. Essentially, the output filter function is $F(x1, x2, x3) = (x1\wedge x2) \vee (\neg x1 \wedge x3)$.

A classical way of attacking Geffe generator is the correlation attack - Google search for "Geffe generator attack" yields a number of relevant results. It looks like this type of attack would be also applicable to your case. 
Another potential attack avenue would be algebraic attacks - output bits are quadratic function of the variables of the internal state, so it might be possible to do linearization attack if you observe enough bits of the output or you have additional data about the content of the registers (e.g. you know decoy bits).

In cryptanalysis, the devil is really in the details, so without posting a full description of the algorithm and a reference implementation, it's difficult to say much more than I already wrote above. This should be a good starting point though.

One more remark regarding attack complexities - while I don't think there is a polynomial time attack on a generator you describe, what we care in practice is concrete (not asymptotic) complexity of the attack. If one can show an attack that has smaller complexity than the best generic attack, it is considered a break of the algorithm.