Officials say Friday that counterterrorism investigators are reviewing the information that mentioned New York, Texas and Virginia as potential targets.
It wasn't immediately clear how the intelligence came to investigators' attention. An NYPD spokesman says in a statement the information "lacks specificity."
In a statement, the FBI said it was working closely with law enforcement agencies and sharing intelligence reports.
Governor Greg Abbott, meanwhile, says his office is monitoring the situation.
"Texans should go about their daily lives as usual, but remain vigilant over the next several days," Abbott said.
Abbott says Texans should report any suspicious activity to state or local law enforcement.
Local security experts say people should take note of the warnings, but not panic.
"The federal government would not be issuing these notices if there was not some chatter in the intelligence community in the possibility of a terrorist attack. That's always there," said retired Lieutenant Colonel Geoffrey Corn, now a professor at the Houston College of Law.
"I think the reality is we have to come to terms with the fact, we can't let it change our lives," said Corn, who points out that a person's chance of being hurt in a terrorism attack is much lower than being injured in many other ways.
In Harris County, the Clerk's office says it met with law enforcement months ago, leading up to the election. It feels like it has the proper procedures in place should something goes wrong.
"The biggest thing we emphasize to (our workers) is call 911 if there is any issues," said Clerk Stan Stanart. "We believe that is the best solution for us."