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."
|Messi, Neymar and Ronaldo headline FIFA Best shortlists|
|Conte thanks Costa after Chelsea exit agreed|
|Zidane will not ´go crazy´ despite Real Madrid slump|
|Ruthless Muguruza and improving Kerber seal Tokyo semi-final spots|
|Aubameyang is very happy here, Bosz assures Dortmund fans|
|Madrid confirm Marcelo hamstring tear|
|I hope he doesn´t score! - Zizou wary of Enzo threat|
|Double for Slater as Storm seal Grand Final spot|
|Major players help teams grow - Simeone happy with selection headaches after Costa move|
|England to name Ashes squad on Wednesday|
|Allegri has faith in misfiring Higuain ahead of Turin derby|
|PSG must prove big-club credentials after spending spree - Draxler|
|Ostapenko strides into Korea Open semi-finals|
|Markram to make Proteas Test debut against Bangladesh|
|Not preventing Neymar´s Barca departure a ´bad decision´ - Rakitic|
|Shanghai Shenhua slam ´misleading´ French media over Tevez interview|
|Tentative Rossi back on track at Motorland|
|Teenager Smith named in England training squad|
|There´s no bitterness – Costa ´cool´ with Conte as Atleti return nears|
|Wallabies omit Korczyk for South Africa and Argentina Tests|
|Dagg out until 2018 to rest knee injury|
|Cummins to skip India T20s to focus on Ashes|
|Cubs take firm control of NL Central with win over Brewers|
|Rams hold off 49ers for wild win|
|Copa Libertadores Review: River put eight past Wilstermann, Lanus through|
|Smith slams Australia batsmen after latest collapse|
|Ronaldo: I´ll get fit if Real Madrid need me|
|Spieth surprised by opening 67 after ´grind´|
|MLB vows teams will ´redouble´ efforts to add safety netting|
|Man United and City have put pressure on Liverpool – Klopp|
|Aubameyang: China talks were a disaster|
|Kyle Stanley grabs lead at East Lake, Jordan Spieth starts well|
|Dembele returns to Barcelona after hamstring surgery|
|EFL set to follow Premier League in transfer window change|
|Aaron Hernandez had severe CTE, researchers say|
|Lions officials defend Gatland´s reign as O´Brien explains criticism|
|Barba, Walmsley shine as St Helens dismantle Salford to close in on semis|
|Howedes a doubt for Juve derby clash|
|Ezekiel Elliott admits to ´lack of effort’ in Cowboys´ loss to Broncos|
|It will go well for Dembele at Barca - Aubameyang|
|Goffin powers through in Metz, Pouille bundled out|
|Abraham denies talk of switch to Nigeria|
|Sauber practice arranged for Ferrari protege Leclerc|
|Federer lauds ´super impressive´ Nadal´s return to summit|
|Defensive worries for bullish Klopp as Liverpool eye Leicester revenge|
|Aubameyang: I no longer dream of Real Madrid|
|52 passes, 11 players, one goal, no West Brom touches - Manchester City´s Guardiola masterclass exam|
|Tsonga sees off Sousa in St Petersburg, Bautista Agut advances|
|Bulls ´willing to work with´ Dwyane Wade on buyout|
|Coetzee keeps Luiten in check at Portugal Masters|
|Gundogan set for swift Manchester City return|
|Costa´s Atletico return: Griezmann primed to shine alongside Atleti´s prodigal son|
|Time to move on from controversial chant, says Lukaku|
|Nadal can inspire Team Europe to Laver Cup glory - Federer|
|Costa´s Atletico return: Torres, Aguero, Falcao and Griezmann and the Rojiblancos´ history of fine f|
|Costa´s Atletico return: Bonucci v Allegri, Beckham v Ferguson and more famous player-manager bust-u|
|Girl injured by Yankee Stadium foul ball ´doing alright,´ father says|
|Wickmayer masters Cornet in Guangzhou|
|Kane will stay a long time, regardless of winning trophies - Pochettino|
|Kuldeep hat-trick sparks Australia collapse in Kolkata heat|
|Ashes hopeful Hameed suffers broken finger|
|England´s second ODI against West Indies washed out|
|I´ll decide who is first choice - Emery putting foot down over Cavani-Neymar penalty spat|
|Rossi declared fit for remarkable Aragon GP comeback|
|Light heavyweight champion Andre Ward retires undefeated|
|Costa´s Atletico return: Henry, Tevez, Rooney and other players who went back|
|No celebrations for Barry unless West Brom take something from Arsenal|
|Strycova dumps out Konta in Tokyo|
|Benzema wants to retire at Real Madrid|
|Atletico Madrid agree Costa deal with Chelsea|