"There's indications we are seeing something of a drift toward the west," said meteorologist Tom Bradshaw, of NWS's Regional Operations Center for the Southern Region Headquarters.
The state's Oil Spill Prevention and Response Program is now warning that some of the oil may wash ashore in the form of "tar balls," possibly in the next two or three weeks.
People along the Texas coast are already bracing for the possibility.
"We're definitely watching the oil leak very closely," said Roshelle Gaskins, of the Galveston Convention and Visitors Bureau. "We really just have to keep watching it closely because those currents, the winds, the storms in the Gulf are ever changing, so we never know. Every day, it's going in a different direction."
Meteorologists with the National Weather Service in Fort Worth are helping other predict the path of the slick. From their office on the 10th floor of the Fritz G. Lanham Federal Building in downtown Fort Worth, 45 meteorologists are keeping their fingers to the wind.
They're watching weather patterns in the Gulf of Mexico to help others predict where the massive oil slick might go.
"We support weather operations at all the offices along the Gulf Coast," Bradshaw said.
"The information that decision-makers are most keying on right now is obviously marine conditions, what are we looking at in terms of winds, 20, 30, 50 miles offshore, what direction are the winds moving? Are they moving the spill toward shore; if so, how fast?" he said.
With Memorial Day less than three weeks away, some North Texans are already beginning to question their summer travel plans.
"We've already had a few coming in wanting to go to Florida or down to the coast, and they're going ahead and taking the information with them and they're kind of doing that 'let's wait and see what happens when it gets a little closer to Memorial Day,'" said Jim Ervin, of AAA Texas in Fort Worth.
Tourism officials along the coast said they hope Texans don't give up on their beach vacations.
"We really encourage people to pick up the phone and get on the Internet and really check what's going on," Gaskins said. "On galveston.com we've got fantastic webcams, so you can look for yourself what the beaches, what the water is looking like and really make that educated decision and not just the assumptions."
Gaskins said officials in Galveston believe the Texas coast is safe.
"We've been speaking with the state, as well as the land office (and) the Coast Guard every day, and, right now, we are still safe and people should come visit," she said.