We report on the interplay between magnetism and superconductivity in La 0.7 Ca 0.3 MnO 3 /YBa 2 Cu 3 O 7 structures. We have grown heterostructures ͑bilayers and trilayers͒ with a constant thickness of the ferromagnetic layer of 40 unit cells ͑15 nm͒ and changing the thickness of the superconductor between 1 ͑1.2 nm͒ and 40 unit cells ͑48 nm͒. The critical temperature of the bilayers decreases when the thickness of the superconductor is reduced below 10 unit cells, thus providing an estimate of the length scale of superconductivity suppression by spin-polarized quasiparticles in YBa 2 Cu 3 O 7−␦ ͑YBCO͒ of 10 nm, much larger than the coherence length. For thickness of the YBCO layer smaller than 4 unit cells; a second mechanism of superconductivity depression comes into play, probably related to the ferromagnetic/superconducting proximity effect. The relative importance in depressing the critical temperature of intrinsic mechanisms ͑quasiparticle diffusion and proximity effect͒ and extrinsic ones ͑intralayer disorder, interface roughness, or reduced dimensionality of ultrathin layers͒ is discussed.