Driving IRF610 from 12v?
Gate drive voltage is fine, but Drain-Source On resistance isn't. Typical RDSon is ~1.2 Ω at 25 °C junction temperature, going up to ~2.5 Ω at 150 °C. At 1.9A you can expect a voltage drop of ~1.2 Ω x 1.9 A = 2.3 V. That will generate 2.3 V x 1.9 A = 4.4 W of heat, which will quickly heat it up - increasing resistance and causing even higher voltage drop and temperature rise.
I recommend using a MOSFET with much lower RDSon and saving your IRF630's for high voltage applications. If you must use the IRF630 then wire several of them in parallel to reduce the total resistance and increase power handling.