On the heels of a presidential speech aimed at drawing more international tourists to the United States, the head of the country’s travel industry lobbying group said government leaders in the U.S. and Brazil — a major feeder market — need to start talks quickly to ease travel requirements to this country.

Once they do, the process to waive visa requirements for Brazilian travelers could take about a year, said Roger Dow, president and CEO of the U.S. Travel Association.

“A miracle could be in 2012,” he said. “Most likely it’s going to be 2013.”

Already, efforts are underway to speed up the process of getting travel visas for Brazilians. At a Greater Miami Chamber of Commerce luncheon Wednesday at Jungle Island, Dow spoke about efforts to increase the nation’s profile as a tourism destination and the likely impact on South Florida.

“As goes the travel industry, so goes Miami,” he said.

President Barack Obama last month issued an issued an executive order to ease the process for obtaining visitor visas for Brazil and China and took additional steps that include promoting national parks and crafting a national tourism and travel strategy.

On Monday, National Park Service Director Jonathan B. Jarvis visited Miami to hear from tourism officials and the superintendents of Everglades National Park, Biscayne National Park and Big Cypress National Preserve.