Edwards lost ground Sunday at Phoenix International Raceway, finishing fourth as Johnson won the race.
"The thing we've got to do is we just have to keep our heads up and go to Homestead," Edwards said. "It's still possible. It's not probable."
Johnson can wrap up the title by finishing 36th or better next week. But Edwards noted that Johnson's teammate, Jeff Gordon, had engine problems on Sunday.
"I can guarantee you that we're just going to go there and give it 100 percent, and hope that something happens," Edwards said. "We saw what happened with (Gordon) today. You never know what could happen."
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GORDON FLAMES OUT: Fighting engine problems all day, Jeff Gordon didn't contend for his first victory of the season.
Gordon's engine began to smoke with 43 laps remaining. Gordon said it was "probably a valve or something."
"I felt it early on," Gordon said. "It was starting to lose some power, and I didn't pay too much attention to it because I was still getting plenty of RPM and the car was still running good. Then all of a sudden it started really going down, and I felt it lose a cylinder."
Gordon didn't finish for the sixth time this year.
"It's the kind of year we've had," Gordon said. "We've had a lot of stuff happen to us. Engines haven't been one of them."
Gordon, a four-time series champion, needs to win at Homestead-Miami Speedway next week to avoid a winless season for the first time since his 1993 rookie year.
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THE HEIDI RACE: With 34 laps remaining, ABC cut away from the race in the Eastern and Central time zones, opting to show "America's Funniest Home Videos" as scheduled.
At that point, two red flags had delayed the race by about 45 minutes.
ESPN2 carried the race's conclusion in the Eastern and Central time zones, and it remained on ABC in the West.
Drivers didn't know about the move until after the race.
"It seems a little odd to me, as big as NASCAR is and as many people watch this sport," said Jamie McMurray, who finished third. "I just can't believe that 'America's Funniest Home Videos' would take priority over us. I mean, I like that show, but I'd rather watch the race."
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DRY DOCK: Martin Truex Jr.'s race ended after 35 laps. His problem?
"Ran out of water," Truex said.
Truex said a clear bag on the nose of his Chevy drove up the water temperature and caused overheating.
"It's just unfortunate," he said. "It's been a tough year with a lot of this kind of stuff. We've had some bad luck."
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STORMY WEATHER: Shortly after Truex's car ran out of water, a brief rain shower swept through, stopping the race for 23 minutes.
"It's crazy; it's raining in the desert," Carl Edwards said during the break. "I definitely don't want to stop. But it's what it is, and we all have to deal with the stuff. I just want to get out and get some green-flag runs.
The rain brought back some happy memories for Kurt Busch, who won the rain-shortened race at New Hampshire Motor Speedway in June.
"Who would have thought, this weather in the desert?" Busch said. "It just reminded me a little bit of Loudon, N.H., when we won in the rain."
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WALLBANGER: Brian Vickers walked away after hitting the wall on the 30th lap. Vickers said "something was loose."
"I haven't the slightest idea what it was, if it was a tire or a mechanical piece of the car," Vickers said. "Luckily it happened on the backstretch and I had time to lean into the impact and absorb some of it because it was a really good, hard hit."
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EARLY PIT STOP: Fifteen minutes before the race started, David Ragan walked into the Phoenix International Raceway press room.
He had to use the restroom and it was the closest available toilet to the track.
Ragan bantered with reporters as he waited in line.
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WEBB LEADS THE WAY: Arizona Diamondbacks ace Brandon Webb was the honorary pace car driver.
Webb, a NASCAR fan from Kentucky, took a high-speed spin with Kurt Busch on Saturday. "I was strapped in and holding on the whole time," Webb said.
Webb said he'd have a light foot on Sunday.
"They told me I'm supposed to go 55," said Webb, who is favored to win his second NL Cy Young Award on Tuesday.
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GOING GREEN: For the first time in a NASCAR event, a hybrid will be the pace car when the Chase concludes at Homestead-Miami Speedway next week.
The 2010 Ford Fusion Hybrid, featuring the debut of Ford's next-generation hybrid system, will pace the Ford 400 along with the Fusion Sport.
The Ford Fusion Hybrid and the Fusion Sport will both be in NASCAR-inspired camouflage for the race. The cars won't be officially unveiled until the Los Angeles International Auto Show three days later.
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