By that thinking, they are coming off a magnificent seven.
The Cardinals won seven of their final nine games last season, winning at Seattle down the stretch — the only visiting team to do that in the last two seasons — and keeping their playoff hopes alive until the end.
Along the way, Palmer, written off by many when he arrived in Arizona before last season, reached some rarefied air. In those final nine games of a 10-6 season, the former Heisman Trophy winner from USC completed 65.7% of his passes (201 of 306) for 2,533 yards with 16 touchdowns, nine interceptions, and a passer rating of 96.5.
During that span, he was one of four quarterbacks to rank in the top 10 in virtually every relevant category. Space will be cleared in Canton for the other three: Peyton Manning, Tom Brady and Drew Brees.
"You could kind of see it coming," Palmer said of how the Cardinals clicked around midseason, emerging as a dangerous team in the NFL's best division. "At one point we just started speaking the same language more often in practice and in meetings. It took a while, but there definitely was a point in time when everybody was like, 'Oh, I kind of get why we're doing this.'"
So a graying quarterback whose career was heading south finds himself in Arizona and rediscovers his love of the game — haven't we seen this movie before?
Yes, and Kurt Warner — at age 37 — wound up leading the Cardinals to their only Super Bowl appearance.
Like Warner, who hit his stride in the second half of the 2007 season, before breaking all sorts of franchise records in 2008, Palmer appears poised for a big year.
"I like just watching him grow in this offense," said Arians, 61, also heading into his second season with the Cardinals. "Last year, you could see his head spinning in the first eight games. He'd wait to see [his receivers] open and then throw it. That's where interceptions occur. And then the last eight games there was a trust factor. The ball was coming out with anticipation. Guys were turning around and catching it, and we were starting to make plays."
That was a welcome change for Palmer, the No. 1 overall pick in 2003, who in recent years had lost some of the enthusiasm he had earlier in his career. He came to Arizona having played in two playoff games in 11 seasons, and having weathered a steady circus of distractions and firings in his decade-plus with Cincinnati and Oakland.
Palmer said there were times when the last thing he wanted to do was talk football.
"I'd talk to my mom and dad, my wife, 'Don't talk to me about it,'" he said after a recent practice. "You want to think about your kids, or think about the Monday night game. It was, 'I don't want to talk about practice. I don't want to talk about what so-and-so did, and who didn't show up.'"
Now, even though he calls the Cardinals "the most comfortable environment I've been in," Palmer doesn't have the luxury of pondering much else but football. He simply doesn't have the time.
"There's definitely times at night when I'm exhausted and we're putting in something new, and I'm thinking, 'Man, I wish I was in year seven of this offense,' and I could be bored of it," he said. "But there are so many things you have to stay on top of. There are so many things that Bruce will say one day, change the next day, then change back. It's like going through notes to find the last thing he said on one play, and he's said four different things. He's always tinkering and always changing things."
All-Pro receiver Larry Fitzgerald, a star on that team the advanced to the Super Bowl against Pittsburgh, noted there's a significant difference between those Cardinals and this year's version.
"Our defense is much stronger now than it ever was," Fitzgerald said. "The way we finished last year is something we can definitely build on. Obviously, we fell short of our goals of making the playoffs. But the way we finished left a solid taste in guys' mouths that we were on the right track and have the right people to make a run."
Under new coordinator Todd Bowles, that defense went from 28th against the run in 2012 to No. 1 last season, no small feat in a power-running division that includes Seattle and San Francisco.
"The guys feel at home," defensive tackle Darnell Dockett said. "Our guys are playing in a system they're used to.… The biggest challenge is, how do you get better when you finish No. 1 against the run? Now we're thinking about how not just to be No. 1 but to be dominant. How can we impose our will in a game?"
Defense can pave the way to titles — consider what Seattle did last season — but the Cardinals are banking on some robust offensive performances from the seasoned Palmer.
"It's a lot harder than a guy like Andrew Luck," the coach said. "You can brainwash them right away. 'This is the only way you do it.' Carson's got ideas, good ideas, so you've got to explain why you don't do it this way against this coverage. There are a lot more questions."
So far, it's working.
"He's worked with some phenomenal guys, guys that embrace his challenges," Palmer said. "You've got to be that kind of guy to play for him. You've got to understand that he's going to say one thing one day, and it's going to change the next. You can't let it frustrate you, you can't go home to your wife and say, 'I can't believe he's doing this!' You've got to understand that that's part of his process, and that's what makes him such a great play caller.
"He's very set in his ways and very stubborn. And I'm very set in my ways and very stubborn. But it's been a really good mesh for two very stubborn, hard-headed guys."
And, even as sunset approaches, they aren't quite ready to call it a day.
Follow Sam Farmer on Twitter @latimesfarmer