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."
|Leaving so soon? Cassano the latest in football´s long list of short stays|
|You´ll miss me! – Mbappe bids farewell to new Manchester City signing Mendy|
|I always wanted Manchester City, says new signing Mendy|
|Cassano quits Verona as saga takes another twist|
|FIR step in after Zebre pull out of Pro12|
|Manchester City spree continues with Mendy arrival|
|Dortmund rule out selling Sokratis to Juventus|
|Birkdale brilliance at The Open: Spieth´s Opta stats stack up|
|Milan coach Montella hopes Scudetto can become ´a concrete goal´|
|Martial is a defender´s nightmare, says Lingard|
|Pedro suffered facial fractures, Conte confirms|
|Rahul ruled out of first Test with viral fever|
|Bale gunning for more Real Madrid success as United speculation ends|
|Ancelotti rules out Vidal sale, Sanches departure ´a possibility´|
|Third Renault test for Kubica in Hungary|
|Van Dijk left out of Southampton´s pre-season trip|
|Froome can remain Tour force - Brailsford|
|Bernardeschi attends Juventus medical ahead of €40m switch|
|Bayern president labels big spending ´a sign of weakness´ amid Neymar rumours|
|Hunt blow for Wallabies, Cheika rules out Lealiifano call-up|
|I sent 10 messages a day - Montella pestered Milan chiefs to attempt Bonucci coup|
|Defoe dreaming of World Cup call-up|
|MLS Review: Timbers, Sounders claim important conference wins|
|Titans guard Tretola treated after getting ´grazed´ by bullet|
|Hall of Famer and first-ever Lakers head coach Kundla dies aged 101|
|Kluber dominant again, but Kershaw and Strasburg exit with injuries|
|Mexico 0 Jamaica 1: Late Lawrence stunner sinks defending champions|
|Vardy: I have no regrets after turning down Arsenal|
|Conte believes Fabregas could be key for Chelsea|
|Phelps loses to great white shark in virtual race|
|Open champion Spieth drinks from Claret Jug again|
|Kahne wins wreck-filled Brickyard 400 in overtime|
|Blanc: Difficult for Verratti to leave PSG|
|Mourinho praises Martial but wants consistency from United star|
|Morata backed for Chelsea success by Spanish duo|
|Zidane: I haven´t asked for a forward amid Mbappe links|
|Henry: Messi´s development not yet over|
|De Boer compares Zaha to Neymar|
|Neymar could take PSG to next level – Blanc|
|Real Madrid 1 Manchester United 1 (1-2 pens): De Gea proves his worth to Mourinho|
|Belotti scores in Torino win, Terry lifts bizarre Cup of Traditions|
|The ´guesswork´ behind Spieth´s stunning Open victory revealed|
|PSG cannot get Sanchez so they go for Neymar - Wenger|
|Murray wins Barbasol Championship for first PGA Tour title|
|Isner completes Hall of Fame hat-trick|
|De Rossi: Juventus have no weaknesses|
|WATCH: Froome spreads the love by helping with marriage proposal|
|Spieth: Nicklaus, Woods transcend the game... I´m nowhere near that|
|He´s staying - Pique eases Barcelona fears over Neymar|
|McIlroy staying patient in quest for more majors|
|Crushed Kuchar pays tribute to ´great champion´ Spieth|
|Teenage lucky loser Rublev crowned Croatia Open champion|
|I´m going to enjoy it more than I´ve enjoyed anything - Spieth savours Open glory|
|Ledecky claims another record-breaking gold, Sun shines in Hungary|
|Bordeaux to sign Arsenal flop Wellington Silva|
|Classy Spieth insists ´emotional´ Kuchar will win a major|
|Markovic free to leave Liverpool, says Klopp|
|The Open Diary: Umbrellas as distress beacons, inflatable palm trees and a lasso|
|Rampant Saints deny Wakefield top-four finish|
|Spieth´s legend forged by stunning Open resurrection|
|I´m over it - Spieth exorcises Masters demons with Open recovery|
|WATCH: Insane hailstorm leads to friendly cancellation|
|Golf´s Grand Slam winners: Open champion Spieth close to joining elite club|
|Froome seals fourth Tour de France title, Groenewegen sprints to victory|
|Stunning Spieth revival seals Open glory at Birkdale|
|BREAKING NEWS: Spieth turns things round spectacularly to win Open thriller|
|Shrubsole seals dramatic World Cup triumph for England as India capitulate|
|Terry lifts bizarre trophy as Aston Villa claim Cup of Traditions crown|
|Advantage Kuchar as Spieth round unravels dramatically|
|Storm monitoring Slater, Smith injury not serious|