If they do they will face the runners-up in Group B, which contains world and European champions Spain plus Netherlands, who lost to the Spanish in the 2010 final, Chile and Australia.
The winners of Group B will face the Group A runners-up.
"We have to work with the players' heads because expectations are going to be so high," said Branco, a fullback with the Brazil team that won the trophy in 1994.
"It's going to tough, because we could end up facing the Netherlands, Spain or Chile."
Coach Luiz Felipe Scolari predictably played down any mention of the knockout stage.
"We have to get past the first round," Scolari said. "Everyone thinks about the second round and forgets that the first stage is important...
"My players are going to be ready for the first stage and then we'll worry about the other teams."
That first round pits Brazil against three teams they have played before at the World Cup.
Brazil open the tournament in Sao Paulo against Croatia, who they beat in their first match of the 2006 finals in Germany.
After a short 300 km trip back to their Rio base they then face a three-hour, 2,250 km return flight to Fortaleza for the second tie on June 17 against Mexico, who they played the last time Brazil hosted the tournament in 1950.
Their third match is in Brasilia on June 23 against Cameroon who they defeated in the group stage in 1994.
"It's always good to start off against a European team because they have to go through an adaptation period in Brazil, and there is a series of things they'll need to implement," said Scolari.
Captain Thiago Silva also talked up their first round opponents.
"We ended up in a strong group, one that gives you goose bumps," the defender said.
"A strong African side, perhaps one of the best. And Mexico has been a tough adversary for us and Croatia is a strong team physically. It's very difficult but we're ready.
"It doesn't matter if we face a strong team early on or later in the tournament, Spain or the Netherlands," he added.
Brazil ended up in the toughest half of the draw but they will still be confident about their chances, having lost only twice in 19 games since Scolari took over in November.
They have scored in all but one of those matches.
Scolari has introduced a solid spine to the team, with Julio Cesar in goal, David Luiz and Thiago Silva in defence, Paulinho the anchor in midfield, and Fred his preferred choice up front.
He has also given his side a self-belief they lacked under his predecessor Mano Menezes and has rallied the often fickle fans behind them. Many players have said the raucous singing was instrumental in helping Brazil win the 2013 Confederations Cup.
Last week Scolari confidently declared, "Brazil are going to win the World Cup in 2014." Now all he has to do is deliver.