England will resume the third day 475 runs in arrears of Australia's mammoth first-innings total, with skipper Alastair Cook (36 not out) and Jonathan Trott (two not out) at the crease.
Swann admits there are no other two batsmen he would prefer to step out onto a placid Emirates Old Trafford pitch after Peter Siddle's double strike late on left England on the back foot.
Siddle removed Joe Root and Tim Bresnan in the final half-hour and it could have been worse with Cook, suffering with a bad back, narrowly avoiding being run out in the penultimate over.
Cook nonetheless remained to help his side to 52 for two and while there is plenty of ground yet to be made up - in a match in which avoiding defeat will retain the Ashes - Swann is certain England's batsmen will do the required spade work.
"I'm 100 per cent behind all our batters to be honest," he said.
"The fact that Cookie is still there is great for us because he's due a big score.
"I don't really watch when he's out in the middle to be honest. I intend to put my feet up and hopefully sleep for six hours.
"Trotty is a world-class player as well and we've got Kev (Kevin Pietersen) and Belly (Ian Bell) and Jonny Bairstow and the rest to come.
"We're very happy with our line-up and the way to win this game is to go past the Australian total, get a bit of a lead and then see what happens on day four and five."
Swann, who earlier took his 17th five-wicket haul in Australia's 527 for seven declared, did reveal that Cook was hampered by a back problem.
Despite the injury the left-hander negotiated the 30 overs England were left after Michael Clarke's declaration - albeit after surviving a dropped chance against Australia off-spinner Nathan Lyon when he was on 15.
"His back seemed to be troubling him a little bit there and so to get through two and a half hours with a sore back as well is great for us," Swann said.
"He'll have a good sleep and a dip in the pool and he'll be right as rain to carry on."
Bresnan's dismissal again opened the debate over England's use of a nightwatchman, although replays showed he did not hit a ball he chose not to review.
Umpire Marais Erasmus agreed with the Australian appeals and, curiously, so too did Bresnan after he attempted to pull at Siddle.
"Bres heard a noise so he obviously thought he'd hit it," Swann said.
"It just goes to show despite what some of you guys think about batsmen walking and not walking, sometimes they genuinely don't know whether they've hit it or not.
"Poor old Bressie - he came off and he couldn't believe the replay when he saw it. He'd heard a noise and presumed it was a bottom edge."
Bresnan's decision not to review was not the most baffling call, however, as instead the players - rather than the umpires - were thrust into the spotlight for their use of the review system.
David Warner made a baffling call to send a nick behind off Swann upstairs, when replays showed he got a healthy nick.
It meant the left-hander firmly established himself as the pantomime villain after his first appearance of the series was greeted by a chorus of boos from the crowd.
Warner missed the opening two Tests after he was punished for punching Root in a Birmingham bar in June, and his belated Ashes debut lasted just 10 balls before he trudged away with the majority of Old Trafford waving him off.
Australia skipper Clarke, who hit his Ashes-best 187 before he became Stuart Broad 200th Test wicket, said he had no problem with the crowd's booing of Warner.
"It's not the first time I've heard a player get booed and it won't be the last," said Clarke, who was jeered by his own fans during England's one-day tour Down Under in 2011.
"It's not just England that it happens - I've been booed in my own country. I know what it feels like.
"I guarantee you it wouldn't have affected Davey one bit.
"He loves it. It's water off a duck's back for Davey."
Despite Australia's strong position, Clarke admitted his side still faced an uphill battle to claim the 18 more English wickets they need to stay alive in their bid to win back the Ashes.
"We have a lot of work ahead. The wicket is pretty flat, there's not a lot of movement there for the bowlers," he said.
"I sit here pleased with the first two days but it's irrelevant if we don't win this Test match.
"We are going to have to work exceptionally hard, even harder than we have over the first two days, over the next three.
"It's not the type of wicket where you can force too hard. The bowlers are going to have to be exceptionally consistent like they were.
"It's the type of wicket that is going to take a lot of time to bowl England out."
- Sports & Recreation
- Alastair Cook
- Tim Bresnan
- Peter Siddle