It is possible that the oil had leaked from a ship involved in the cleanup, he said, as some of the oil-water mix collected during the response operation is being taken to a processing company near Galveston. The Coast Guard is still conducting tests.

For now, many people who live and work along the Texas coast say they are not in a panic, adding that tar balls wash up all the time. But that does not mean they think this will be the end of it.

“I figure they’ve got their head buried in the sand if they don’t think we’re going to get it over here,” said Carol Dickerson, who works at Blue Water Bait Camp in Crystal Beach, Tex. “There’s just too much oil, and I know that we’re going to get it eventually.”

The worries in New Orleans are more immediate.

Since the spill began, the city has been in a difficult situation. It has become the headquarters for the area command and is frequently the backdrop for news reports.

But the city has constantly had to give geography refreshers to hesitant tourists, reminding them that New Orleans has no beachfront and is a two-hour drive from the state’s southern coast, where most of the oil has washed up.

Those messages are now more complicated.

“The situation changes a little bit now that tar balls have hit the lake,” said Kelly Schulz, a vice president of the New Orleans Convention and Visitors Bureau. “We’re working on that as we speak.”

The counterclockwise currents in Lake Pontchartrain suggest that if oil did enter in heavier concentrations, it would travel along the lake’s northern coast, which is heavily populated in some areas, before coming back around to New Orleans, Ms. Rheams said.