Legislative approval for the deal remains uncertain and might depend on Gov. Mark Dayton and Republicans finding an initial fix for the state's $5.1 billion deficit.
The July 1 deadline was included in terms made public in May and Rep. Morrie Lanning, R-Moorhead, the chief House author of stadium legislation, told the newspaper "that's a deadline we all have."
"Why would we start from scratch again?" he said. "Nobody's holding a gun to my head. Nobody's holding a gun to (the Vikings') head.
"If those deadlines come up and somebody says, 'Let's take a walk, and not come back,' that could happen," Bennett told The Star Tribune. "All I can tell you is generally we are in a good position. If it doesn't happen, it doesn't happen."
Wilf added that a new facility would give Minnesota the opportunity to host events like the Final Four and the Super Bowl. He also downplayed the notion that his public statements about keeping the Vikings in Minnesota is hurting his leverage, especially with buzz building about an NFL team landing in a new stadium in Los Angeles.
The Associated Press contributed to this report.