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 | FalkirkFalkirk | 14 | 10 | 2 | 2 | 27 | 9 | 18 | 32 |
| 2 | Livingston | 14 | 8 | 5 | 1 | 19 | 10 | 9 | 29 |
| 3 | Ayr UnitedAyr | 14 | 7 | 4 | 3 | 22 | 14 | 8 | 25 |
| 4 | Partick ThistlePartick | 14 | 6 | 5 | 3 | 17 | 9 | 8 | 23 |
| 5 | Queen's ParkQueen's Park | 14 | 6 | 4 | 4 | 16 | 15 | 1 | 22 |
| 6 | Raith Rovers | 14 | 4 | 3 | 7 | 13 | 18 | -5 | 15 |
| 7 | Hamilton AcademicalHamilton | 14 | 4 | 3 | 7 | 19 | 25 | -6 | 15 |
| 8 | Greenock MortonMorton | 14 | 3 | 5 | 6 | 11 | 19 | -8 | 14 |
| 9 | Dunfermline AthleticDunfermline | 14 | 3 | 3 | 8 | 11 | 15 | -4 | 12 |
| 10 | AirdrieoniansAirdrieonians | 14 | 1 | 2 | 11 | 6 | 27 | -21 | 5 |
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