On Sunday, the first one arrived.
Cleveland played perhaps its best all-around game since returning to the league in 1999, beating the Detroit Lions 24-14 to give Davis his first NFL coaching victory.
"Not one moment since I've been here have our players said, 'Are you sure this is the right thing to do?"' Davis said Monday. "They want to win. They've bought into it."
Davis couldn't have scripted a better first win if he tried.
The Browns' defense intercepted seven passes from former teammate Ty Detmer and swarmed all over the field. Quarterback Tim Couch threw three TD passes and rookie James Jackson rushed for 124 yards _ Cleveland's first 100-yard game since 1995.
The special teams, whose breakdown on a late kickoff cost the Browns a win in Week 1 against Seattle, chipped in by stopping Detroit's Desmond Howard from busting any long kick returns.
An aggressive defense. A balanced offense. A strong running game and efficient specials teams. It was as if the Browns tore a few pages from Davis' "How-to-Win" manual.
"I don't think in my two years that we had a game like that, where I felt like we really won the game in all phases," said safety Percy Ellsworth, who had one of Cleveland's team record-tying seven picks.
"Seven interceptions may seem like they gave it to us, but all three phases played well. It feels great."
Especially for Davis, who was hired in January to turn around a franchise that won just five games in two seasons under Chris Palmer.
As he sprinted off the field following the game, Davis, his cheeks flushed with victory, pumped his fist and acknowledged the Browns' fans who are growing more and more fond of the new coach.
Once he got to the locker room, Davis helped hand out game balls to team owner Al Lerner and Couch before the Browns awarded one to their first-year coach.
"He was very excited," said safety Earl Little, who played for Davis at Miami. "But he doesn't change much. That's the thing about Butch. He's straightforward, but he gets excited just like a player."
Davis, who had a lot to be happy about following the win, was touched by his player's gesture.
"I know how hard it is to win and how much they've bought into what our coaching staff is trying to do," he said. "It means a lot."
Through two games, the Browns look like a much better team under Davis.
Cleveland's defense, which held the Seahawks to three field goals in the season opener, gave up just one TD and put Detmer through the longest day of his playing career.
Davis, a former defensive coordinator in Dallas, was particularly pleased that Cleveland held Detroit's James Stewart to 71 yards and the Lions to just 82 yards rushing.
Davis also likes the attitude he's seeing out of his defense.
"I like the way we're starting to get off blocks," he said. "I can't stand defensive players who magnetize to offensive lineman. I want guys to shed and escape and get off, and have a nasty attitude when we get there. And we're starting to do some of those things."
Couch wasn't spectacular but didn't make many silly mistakes, finishing 12-of-20 for 138 yards and three TDs _ one to backup center Shaun O'Hara and one to Kevin Johnson, who had been the subject of trade rumors last week to Kansas City.
"At least he didn't throw it to them seven times," Davis said of Couch while making a little dig at Detmer.
And with Jackson getting stronger as the game progressed, the Browns finally ran the ball like the old Browns teams of Jim Brown, Marion Motley and Leroy Kelly used to.
"Besides the yardage, he ran extremely hard," Davis said of Jackson, whom he coached at Miami. "He ran with power and authority."
Davis knows his team has a long way to go and that a lot can happen in the next 14 weeks. But he likes where the Browns appear to be going.
"I'd say we're pretty much on track," he said.