Alex Pike’s team have recorded just one win so far this season.
That came in the last round as they knocked out Western League Bridgwater Town 1-0.
In the premier division of the Southern League, Borough have had a miserable time – losing their opening seven games to leave them marooned at the bottom without a point.
Swindon Supermarine, who play one level lower in the west division, are unbeaten so far this term.
And they are expected to give the home side plenty of problems.
Pike knows his team will have to defend far better than during their 4-2 Privett Park defeat at the hands of Farnborough in midweek.
The Borough defence had a complete meltdown at the start – conceding four goals in the opening 24 minutes.
While they restored some pride after that – with goals from Aaron Dawson and Luke King – they can ill afford a repeat if they want to advance in the cup.
Once again the pressure will be on the hosts and it is how they handle it that will be the key.
Pike admits the situation is a difficult one.
‘Our hands are very much tied at the moment with us being under a transfer embargo,’ said the Borough boss.
‘The club is working hard to try to get us off it and give us a chance.
‘Swindon Supermarine are flying at the moment and they will be relishing the game.
‘My job is to try to pick my players up because confidence is running low at the moment.’
By contrast, AFC Portchester make the long trip to Truro City feeling they have little to lose.
The Royals pulled off a shock 1-0 win over Southern League premier division Dorchester Town in the last round on the Cup.
Manager Ian Saunders insists his side are going to Cornwall to enjoy and make the most of the occasion.
He feels few people expect Portchester to get a result, so there is no pressure on them.
‘Truro are fifth in National League South and who have won their past six games,’ said Saunders.
‘We are under no illusions as to the difficulty of the task.
‘At the same time we intend to go and do ourselves proud.
‘It is the FA Cup and history has shown anything can happen.
‘We have got a good blend of experience and youth in our team and players capable of causing them problems.
‘As a squad we are very content where we are at the moment.
‘Maybe we can go and ruffle a few feathers.
‘Nine times out of 10 Truro will win but who knows what might happen if Lady Luck smiles on us.’
Don’t miss the Sports Mail on Sunday morning for a full round-up of all the weekend’s non-league results.
And grab The News on Monday for all the reaction to those fixtures, plus pictures from a feature match.