The 61-year-old took over at the bottom-placed club last week following the sacking of Jim McIntyre.
"I wouldn't have taken the job if I didn't think there was a chance," said Jefferies. "There are enough games and enough points."
Dunfermline host St Mirren at East End Park on Saturday.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Dundee UnitedDundee Utd | 36 | 22 | 9 | 5 | 73 | 23 | 50 | 75 |
| 2 | Raith Rovers | 36 | 20 | 9 | 7 | 58 | 42 | 16 | 69 |
| 3 | Partick ThistlePartick | 36 | 14 | 13 | 9 | 63 | 54 | 9 | 55 |
| 4 | AirdrieoniansAirdrieonians | 36 | 15 | 7 | 14 | 44 | 44 | 0 | 52 |
| 5 | Greenock MortonMorton | 36 | 12 | 9 | 15 | 43 | 46 | -3 | 45 |
| 6 | Dunfermline AthleticDunfermline | 36 | 11 | 12 | 13 | 43 | 48 | -5 | 45 |
| 7 | Ayr UnitedAyr | 36 | 12 | 8 | 16 | 53 | 61 | -8 | 44 |
| 8 | Queen's ParkQueen's Park | 36 | 11 | 10 | 15 | 50 | 56 | -6 | 43 |
| 9 | Inverness Caledonian ThistleInverness | 36 | 10 | 12 | 14 | 41 | 40 | 1 | 42 |
| 10 | Arbroath | 36 | 6 | 5 | 25 | 35 | 89 | -54 | 23 |
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