SAN FRANCISCO — Maybe the mistake made about the Chicago Bears this season, at least within the organization, was thinking that the window of opportunity was still open for the loser of Super Bowl XLI.

Just three years later, the nucleus of that team remains intact, and that’s one of the challenging things in the NFL -- maintaining a core group of players long enough to remain competitive for a stretch. General manager Jerry Angelo made the bold move of trading for quarterback Jay Cutler in April and seemingly finding a solution to a decades-old issue for the franchise -- and making the Bears one of the teams to beat in the NFC. Or many people thought.

At the midway point of the season, the Bears find themselves 4-4 with three losses in their past four games, including blowout defeats against Cincinnati and Arizona. Coach Lovie Smith has come under fire, and he’s now 20-20 since the Super Bowl loss when he ran off defensive coordinator Ron Rivera to promote longtime friend Bob Babich and famously said, “Trust me.” The Super Bowl hangover is well known, at least over the last decade, as the loser of the big game struggles the next season. But in the 20 Super Bowls prior to the Bears’ appearance, 18 of the losing teams returned to the playoffs within two seasons. In failing to do so, the Bears have joined the 2002 Oakland Raiders and the 1998 Atlanta Falcons, company no one wants to keep.

The Bears have mistakenly said they’re even at this point because their record is .500, ignoring the fact that the Minnesota Vikings are 7-1 and running away with the NFC North. They point to two remaining games with the Vikings and insist it gives them an opportunity to play catch-up quickly. True. It’s also a chance to lose by three touchdowns to another opponent.

So the Bears enter tonight’s meeting with the 49ers (3-5) at Candlestick Park with the belief that the short week is the perfect antidote to their loss to the Cardinals, a chance to get back on the field in a hurry and get right. But their only victory since Oct. 4 has come against the lowly Cleveland Browns, and right now it’s hard to put much stock in what they’re saying.

“When you lose, all these things come up. Leadership? Are we ready to play?” Smith said. “All the questions you ask, they come up when you lose. When you win, they don’t. Four times this year, they’ve come up. I’m interested in this next time to see exactly what we have. We have leaders. It’s natural to get down when something bad happens, but you can’t stay down, and that’s where we are. But we don’t have to stay there, and that’s what we’re going to do.’’

The 49ers have stumbled of late, losing four in a row. But they had close losses at Houston and Indianapolis and squandered a lead last Sunday at home against Tennessee. Alex Smith has given the offense a little buzz, but San Francisco has been done in by some fluke plays, the kind that don’t derail winning teams. At one point, the Niners led the NFC West, but they now find themselves tied with Seattle and trailing the Cardinals by two games. Time is running out on them, although the schedule does lighten up in the second half with games vs. Jacksonville, Seattle, Detroit and St. Louis.

“I am excited about the game, excited about the challenge and excited that the country will have a chance to see the 49ers, the young 49ers, come of age in the second half of the season,” coach Mike Singletary said. “I am excited about that.”

Asked what he meant about coming of age, Singletary said you’re going to have to tune in.

“All I can say is that you just have to watch the game,” he said. “I’m sure you will ask the questions afterward, but you just have to watch the game. That’s all I can tell you.”

The Bears are putting a great deal of pressure on their defensive front to improve, and the opportunity should be there. The team is expecting tackle Tommie Harris to bring his best — whatever that is — following his ejection for slugging the Cardinals’ Deuce Lutui last week. The Niners are missing left tackle Joe Staley, and the Bears believe Alex Brown can win his battle with fill-in Barry Sims. Adam Snyder is a reserve at right tackle with Tony Pashos out for the season. The pass rush has been nonexistent for the Bears in recent weeks, and if they can kick start it tonight, the secondary that’s dealing with injuries will look better.

The loser of this game won’t be mathematically eliminated from anything, but it will be tough for it to recover and reach the postseason. There’s a lot on the line. It’s worth pointing out that some of Jay Cutler’s worst efforts this season have been in prime time and on the road, at Green Bay and Atlanta.

“Prime-time games, I think some teams play up and some teams play down,” Singletary said. “I think, for us, we’ll play up. I don’t know anything else about how Chicago responded. I just know that…we’ll be ready to play.”

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