Go to Mexico for H1 visa stamp

Hello all,
I need some urgent help here.

Does anyone have recent visa experience in Mexico? I am a H1 worker and I need to travel to Europe for a meeting. My lawyer suggested me to get my H1 visa stamp from third country. Can I go to Mexico and apply visa stamp and get back to US territory in the same day? I read somewhere that it will take several days for the officers to review the visa.

Your help will be greatly appreciated!