The official was dismissive of the deputy's criticisms and affirmed that Fifa would not let local laws diminish the tournament's commercial potential
Several high-profile politicians, including 1994 World Cup winner and current socialist deputy Romario, have denounced Fifa for its attempt to circumvent federal legislation for what they see as commercial benefits.
The organisation has pointed to laws discounting match tickets for certain low-income groups and the prohibition on the sale of alcohol in stadiums as particular problems as they negotiate the 'General Law of the 2014 World Cup'.
In response, Valcke insisted that Fifa had no intention of backing down on any demands and would not be swayed by complaints.
"In the end, there will not be any victors. Brazil will not defeat Fifa, Romario and other deputies will not defeat Fifa. Either we do things together or we will not win, the World Cup will be in Brazil and we want it to go well," the official fired to O Estado.
The secretary maintained that Brazilian authorities had agreed to the compromises when they received the World Cup in 2007, and that he did not understand the posture of Romario, who had accused Fifa of "wanting to run things in our country" on Wednesday.
"That leaves me sad and perplexed. There is nothing new in what we are asking. Everything was in the documents signed in 2007," Valcke said.
"[Fifa] has already made concessions in several areas and the moment has come to stop talking about laws and regulations."
Valcke will meet Brazilian president Dilma Rousseff and new minister for sport Aldo Rebelo next week, to finalise details of the General Law.
Communist Party member Rebelo has a reputation within Brazil as being critical of the impact of business on football, and has previously stated that changes to legislation would have to go through the parliament.