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 | 35 | 21 | 9 | 5 | 69 | 22 | 47 | 72 |
| 2 | Raith Rovers | 35 | 19 | 9 | 7 | 53 | 42 | 11 | 66 |
| 3 | Partick ThistlePartick | 35 | 14 | 13 | 8 | 62 | 50 | 12 | 55 |
| 4 | AirdrieoniansAirdrieonians | 35 | 15 | 7 | 13 | 44 | 42 | 2 | 52 |
| 5 | Greenock MortonMorton | 35 | 12 | 9 | 14 | 42 | 43 | -1 | 45 |
| 6 | Dunfermline AthleticDunfermline | 35 | 11 | 11 | 13 | 40 | 45 | -5 | 44 |
| 7 | Ayr UnitedAyr | 35 | 12 | 7 | 16 | 50 | 58 | -8 | 43 |
| 8 | Queen's ParkQueen's Park | 35 | 10 | 10 | 15 | 48 | 56 | -8 | 40 |
| 9 | Inverness Caledonian ThistleInverness | 35 | 9 | 12 | 14 | 38 | 39 | -1 | 39 |
| 10 | Arbroath | 35 | 6 | 5 | 24 | 35 | 84 | -49 | 23 |
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