Managing director Richard Neall, who led a management buyout of the firm from Peterhouse last year, said: 'We are the principal contractor on the site and, initially at least, the buck stops with us.
'I'll probably be dealing with this for the next couple of years, but we are confident and we have the support of the banks.'
Project engineer White Young Green declined to comment.
A Network Rail spokesman said Tesco would face a bill 'running into millions of pounds' for blocking the line, which it will pass on to its construction team.
Jackson will also have to replace the rail and sleepers in the tunnel crushed by thousands of tonnes of rubble. The clearup operation is running 24 hours a day but the line could be closed for another three weeks.
A senior source at one rival rail contractor said: 'The penalties will be enormous. If you're 10 minutes late handing over a bridge at peak time on the West Coast Main Line it costs you £150 a minute per train delayed. It would be at least £100 a minute on the Chiltern line.'
Nearly a quarter of the Gerrards Cross tunnel will have to be replaced after Health and Safety Executive inspectors found further evidence of failure around the 29 arch sections that collapsed. The reinforced concrete sections were manufactured by Northern Irish firm Macrete.
A Network Rail spokesman said: 'The HSE has so far identified between five and 10 1.5 m-long sections on either side of the collapse that will be have to be replaced.
'We don't know how many more might have to be replaced yet, as the spoil from the tunnel has blocked efforts to inspect it all.'
Mr Neall said: 'Several more units will have to come out and further sections could be identified when the HSE has carried out a detailed inspection of the tunnel.
'We took a health and safety decision straightaway not to let anybody in the tunnel and it has been a very complex procedure to lift the fallen sections out through the hole.
'We will demolish further sections from the outside.'
But the cause of the collapse remains a mystery and a detailed forensic examination is under way. Costain, which is building the Tesco store, has stopped work until the HSE has signed off the tunnel.
Mr Neall added: 'We're looking at every element of the project from the design, the manufacturing and reinforcement of the concrete units themselves, how they were constructed and the method of placing the fill, but at this stage we simply don't know.'
The tunnel arch is formed using over 300 precast concrete half sections - each weighing 21.5 tonnes - which link together to form a three-pin arch. Jackson backfilled over this to create a level surface for the new Tesco store.
The collapse happened at the Marsham Lane end of the site, around 200 m away from the store at the Packhorse Road end.
The job slowed due to wet weather last summer and delays in gaining design approval for the Packhorse Road bridge strengthening work.
Gordon Masterton, senior vicepresident of the Institution of Civil Engineers, said: 'The critical stage is when you start backfilling around the arch. If you buried an eggshell in the sand you would have to build sand up from the sides rather than put it on the top.
'It is more likely a combination of two or three factors - they will be looking at the soil structuring, design and whether the materials used match the design assumptions.'