  We study one-parameter families of quasi-periodically forced monotone
interval maps and provide sufficient conditions for the existence of a
parameter at which the respective system possesses a non-uniformly hyperbolic
attractor. This is equivalent to the existence of a sink-source orbit, that is,
an orbit with positive Lyapunov exponent both forwards and backwards in time.
The attractor itself is a non-continuous invariant graph with negative Lyapunov
exponent, often referred to as "SNA". In contrast to former results in this
direction, our conditions are C^2-open in the fibre maps.
  By applying a general result about saddle-node bifurcations in skew products,
we obtain a conclusion on the occurrence of non-smooth bifurcations in the
respective families. Explicit examples show the applicability of the derived
statements.
