Dean Elgar believes South Africa have exposed weaknesses in the England side that the tourists can continue to exploit for the remainder of the Test series.
The Proteas are heavy favourites to tie up the four-match rubber at one apiece after setting England a huge target of 474 with two days of the second Test at Trent Bridge remaining.
Opener Elgar was the first of three batsmen, along with Hashim Amla and captain Faf du Plessis, to score a half century as South Africa made their hosts pay for conceding a 130-run deficit in the first innings.
The declaration arrived late on Sunday after the tourists reached 343-9, with Alastair Cook and Keaton Jennings forced to survive a menacing burst from Morne Morkel and Vernon Philander before the close.
With six full sessions to see out having been dismissed in 51.5 overs first time around, Elgar does not rate England's prospects of escaping without defeat particularly highly.
"According to the stats, it shouldn't happen," he told reporters, acknowledging that a successful run chase from England would comfortably represent a world record.
"The wicket is getting better but the odd ball is squatting a bit. It will be hard work for us to get 10 wickets but our bowlers are looking forward to it.
"We don't want an easy Test victory – it has to be hard work to win a Test.
"We have opened up a few cracks in their side and will be brilliant for us in the future in this series. I'm not surprised by the swing since [the 211-run defeat in the] Lord's Test.
"We've been playing brilliant cricket for two or three years as one of the best teams in the world."
Moeen Ali helped himself to four wickets as South Africa hit out during the evening session and the all-rounder believes much of England's hopes of keeping a series lead for the third Test at The Oval rest upon Cook.
The former captain overturned an lbw dismissal on review first ball from Morkel before he and Jennings edged nervously to 1-0 at stumps.
"We have got some very good batters who are capable of doing it," Moeen said of an innings where significant scores for either Jennings or Gary Ballance would be timely with regards to their long-term prospects of remaining in England's under-scrutiny top three.
"Cookie, when he gets in, is hard to get out and hopefully we will see that. We need a good foundation to bat six sessions.
"The top three can be very solid and bat time, then we have Joe Root in good form. But we will have a chat before play."
|Ashes newcomer Bancroft thought Test chance was gone - Voges|
|Warner suffers injury scare ahead of Ashes|
|Guardiola dismisses Champions League favourites tag|
|Jackson excited about Gordon´s return: I get to open a new toy|
|Nuggets head coach Malone suspended for one game|
|Steelers OT Gilbert handed four-game PED suspension|
|Prior hits back at ´ridiculous´ claims as Lyon hopes Australia end careers|
|Dolphins QB Cutler placed in concussion protocol|
|Navratilova leads tributes to ´amazing´ Novotna after her death at 49|
|Brighton and Hove Albion 2 Stoke City 2: Gross, Izquierdo extend home unbeaten run|
|Dimitrov braced for Australian Open expectations|
|Broncos fire offensive coordinator Mike McCoy|
|England won´t suffer Gabba ambush, Malan claims|
|Rose in contention to face Dortmund as Pochettino denies ´issue´ with defender|
|Benzema knows he can give more – Zidane|
|I´ve fulfilled my dreams already – Klopp has no plans to coach Barcelona|
|Memorable Ashes Moments: Unlikely saviour Agar falls agonisingly short|
|Wallabies coach Cheika faces investigation|
|The Ashes: Australia squad profiles|
|Aubameyang will face Tottenham, Bosz confirms|
|Klopp expects Matip to face Chelsea, Lallana return getting ´nearer´|
|Brown could return for England, Underhill out|
|Haye´s rematch with Bellew off due to bicep tear|
|The Ashes: England squad profiles|
|Gatland vows not to rise to New Zealand media barbs|
|Berizzo looking to former Red Aspas to provide lessons for Sevilla|
|Mangala ready to pounce, but realistic on Man City playing time|
|The Ashes: How the urn will be won - the case for Australia and England|
|Innovation key as WTA Media embraces evolving viewing habits|
|Trump calls for Lynch to be suspended as anthem row returns|
|Mendy injury means Aguero or Jesus for Guardiola|
|Kohli proud of India after almost snatching Kolkata win|
|The Ashes: Key contests in the battle for the urn|
|Guardiola sends ´big hug´ to ´amazing, so gentle´ Pulis|
|Tavecchio quits as head of FIGC, claims board have refused to resign|
|Benedetto facing Argentina World Cup KO with cruciate injury|
|Hansen hails All Blacks progress|
|Kohli´s record century precedes Bhuvneshwar heroics, but Sri Lanka cling on|
|Shape up! Heynckes reveals demand to Bayern star Vidal|
|Australia hope to open England ´scars´ in Brisbane|
|Smiling Broad sports bruise after golfing mishap|
|Ramos sits out Madrid trip to APOEL|
|West Brom sack Pulis after wretched run|
|Ball fighting fit ahead of Ashes opener at the Gabba|
|Murray should appoint Delgado as Lendl replacement - Henman|
|Former Wimbledon champion Novotna dies aged 49|
|Lloris wants Spurs to forget title and focus on top four|
|Pogba no Gerrard yet, says Benitez|
|Pearce released from Roosters contract|
|Expect to get six ducks – Paine reveals Rogers´ Ashes advice|
|Lyon: I don´t care if Stokes plays Ashes|
|Curry´s offensive explosion leads Warriors past Nets|
|Ball records second triple-double to join Magic, West in record books|
|Patriots, Ravens win among multiple blowouts|
|Flyers´ Gudas suspended for 10 games for violent slash|
|Two-time NBA All-Star David Lee announces retirement|
|Guardiola will ´kill´ City stars if they get complacent|
|Bills coach McDermott to ´evaluate´ quarterback position|
|LeBron on Kaepernick controversy: I don´t respect the NFL|
|Ibrahimovic: My injury was worse than people know|
|Russell to leave Warriors at end of season|
|Cook cruises to first PGA Tour win|
|Truex wins first NASCAR championship|
|Cardinals´ Fitzgerald now fifth all-time in receiving yards|
|Icardi like a ´raptor pouncing on its prey´, says Spalletti|
|Tired Goffin insists: ´I will be ready for Davis Cup final´|
|In-form Chelsea have regained hunger - Conte|
|Stones can bounce back stronger - Kompany|
|Guardiola ready to risk Kompany for Man City after Stones´ injury|
|City style suits me and thrills neutrals, says De Bruyne|