on one's shoulders
As one's responsibility, as in The king carries his entire country on his shoulders, or The success of the conference rests on Nancy's shoulders. This metaphoric use of shoulders as the burden-bearing part of the body dates from the late 1300s.
Words nearby on one's shoulders
on one's own,
on one's own account,
on one's own time,
on one's part,
on one's say-so,
on one's shoulders,
on one's soapbox,
on one's tail,
on one's toes,
on one's uppers,
on one's way