A little more than a week after dramatic flooding played out in Phoenix, Tucson and Las Vegas, residents and emergency officials in the U.S. Southwest prepared for another possible onslaught of rain.

Meteorologists warned people from southeast Arizona into southwest New Mexico to be ready for the remnants of Odile, which slammed into Mexico as a hurricane last weekend.

New Mexico declared a state of emergency Wednesday night, opening the lines for financial and personnel support to flow from the state to local governments in case of a flood.

"We're taking proactive measures to be ready for this storm, including pre-positioning key National Guard personnel and equipment. I encourage all New Mexicans to be cautious and safe throughout this storm," Gov. Susana Martinez said.

Although no major problems had been reported yet, some places along the U.S.-Mexico border had already picked up several inches of rain by Wednesday evening, and more is ahead. The National Weather Service (NWS) issued Flash Flood watches for a large portion of Arizona, southern New Mexico and far southeastern Nevada and California. Some creeks were already bursting through their banks.

(FORECAST: Track the Southwest Flood Threat)

In Arizona, Tucson could see the heaviest rain, but forecasters warn people in Phoenix should expect rain and gusty wind, too.

People appeared to be listening to the warnings, and were taking advantage of free sandbags in Tucson, Mesa and Phoenix. Traffic backed up at two parks in Tucson where they were being given out, the Associated Press reports. 

"It flooded my whole property, my horse pens, and my garage was under about 2 feet of water," Roger Fuller told the AP. "This time around, we're trying to keep the water off the property. Hopefully, it will work."

Similar scenes played out in New Mexico, particularly in Las Cruces, where the heaviest rainfall is expected. Firefighters passed out sandbags to concerned residents hoping stave off potentially devastating flash flooding.

"I don't remember it being this wet in a long time, probably years," Las Cruces resident Gretchen Taylor told the Las Cruces Sun-News. "We're not used to that and I wonder a little if the city is really prepared for a big deluge."

This will be the second time in less than two weeks a tropical system that impacted Mexico will take an unusual path into the desert Southwest. On September 8, the remnants of Norbert moved into the region, killing two people in Tuscon, and damaging interstates near Las Vegas.

MORE ON WEATHER.COM: U.S. Southwest Flooding Early September 2014