A slender one dimensional (1D) model for filaments of liquid crystalline polymers (LCPs) is applied to simulate isothermal fiber spinning of materials with internal orientation. The focus is on the hydrodynamic-orientation interactions in spinning flows, isolated from other significant spinline effects of temperature, crystallization, and phase changes. Spun fiber orientation (in particular, birefringence) is deduced from first principles along with fiber diameter and velocity. One result of our modeling and simulations is that, in isothermal spinning, the microstructure (orientation tensor) is weakly radially dependent and can be calculated from 1D models. Families of numerical steady state fiber spinning solutions, together with their linearized stability, are presented. These calculations reveal upper bounds on throughput in terms of the critical draw ratio, above which the process is unstable. The effects on stability due to LCP parameter changes are thoroughly investigated. We find enhancement of the effects of LCP kinetic energy or relaxation can either stabilize or destabilize steady spinning solutions, whereas enhanced anisotropic drag is always destabilizing. Evidence is given for a preferred degree of upstream LCP alignment at which the critical draw ratio achieves a maximum, indicating an important role played by near-spinneret conditions in increasing throughput.