On Sunday an influx of sub-tropical moisture will make its way into New Mexico. This is the result of Tropical Storm Ileana and a low pressure system building over Northern California. This moisture will allow for widespread storms on Sunday and Monday. Most of the state, with the exception of Southern New Mexico, can expect to see rain on Sunday and Monday.
On Monday, the low pressure system moves from Northern California to the Great Basin. This shift in the low pressure will also shift the moisture in New Mexico to the East. The rain chances on Tuesday will follow the moisture. Resulting in Eastern New Mexico having the best storm chances in the middle of next week.