The Hearts manager insisted his side can't afford to take anything for granted in the race for a top-six place – despite St Johnstone's defeat to Dundee United last night.
Saints lost out to Peter Houston's side at McDiarmid Park courtesy of a late Jon Daly header, leaving the way open for Hearts to claim the sixth and final spot in the top half of the SPL table this weekend.
A draw over Kilmarnock at Tynecastle would be enough to secure a top-six place although Jefferies is targeting the full three points.
However, the Hearts boss warned his side that Killie, who are fighting for their SPL survival, will be determined to put a spanner in the works when they arrive in the Capital on Saturday.
Jefferies said: "We will give it our all to get the right result against Kilmarnock.
"The boys all know what is at stake and they've had a wee lift with the result last night and the way that they came back to take a point against St Mirren on Saturday.
"That is a really difficult place to go and you have to remember that Hearts have not had the best of records against them in recent seasons.
"It's been put back into our hands now and we've got to make sure that we grasp it and make it count.
"This is the situation that we wanted, we have got to make sure that we get the win and put on a show for our supporters as well. We will be playing another team who are fighting for their lives in the SPL right now but they are playing well right now and we have got to make sure we don't think that it is done and dusted."