We provide a scaling framework describing the different regimes attained by a slit-confined polymer, undergoing an external pulling force f(el,slit). Linear and nonlinear force-extension relations are discussed in the limit of small and large elongations, resorting to the notion of self-avoiding pancakes. The crossover to a channellike behavior allows to explain the scaling of f(el,slit) as a function of the confinement h observed in recent tug-of-war experiments. The theoretical analysis provides also a qualitative explanation of DNA relaxation and coil-stretch transition experiments performed in nanoslits.