It had been scheduled to come up for council vote Jan. 9.
"We can tweak the tools that are used," White said. "We both share the same goal of billboard removal."
White met Thursday with representatives of Scenic Houston and a legal expert on billboard regulation, Bill Brinton. Scenic Houston had paid for Brinton to fly from Florida to meet with White.
Despite the holiday slowdown, Scenic Houston representatives have also met with 10 of 14 council members.
The billboard proposal grew out of an attempt by the city to settle legal disputes with Clear Channel Outdoor, one of the main billboard owners in Houston. The agreement would speed up the dismantling of smaller billboards, while allowing the company to move some medium-sized boards to new spots. The city's 23 scenic districts, and local residential streets, would be off limits.
Mayor Bill White and Councilwoman Pam Holm had touted the immediate gains: 881 billboards taken down in 2008, versus 687 scheduled to come down by 2013.
But critics said the administration had offered the industry a major loophole: a "relocation provision" that would allow Clear Channel to move 466 medium-sized billboards to new locations.
"On the surface, it's pretty good public relations," said Councilman Peter Brown. "Put up 466, but take down 800-odd billboards. But most of those 800 some are coming down anyway, by attrition, or they're blocked by trees or new construction. They're just not marketable anymore."
Brinton, the Florida expert, said the relocation provision "violates a core principle of billboard reduction ... freeze everything in place. Don't let it move, don't let it be rebuilt."
Brinton said Houston's original policy was working over time. Through attrition, billboards were coming down because of lease expirations, new development, weather damage and market downturns.