In the standard quasar model, the accretion disk obscuration is due to the canonical dusty torus. Here, we argue that a substantial part of the quasar obscuration can come from the interstellar medium (ISM) when the quasars are embedded in compact starbursts. We use an obscuration-unbiased sample of 578 infrared (IR) quasars at z~1-3 and archival ALMA submillimeter host galaxy sizes to investigate the ISM contribution to the quasar obscuration. We calculate SFR and ISM column densities for the IR quasars and a control sample of submillimeter galaxies (SMGs) not hosting quasar activity and show that: (1) the quasar obscured fraction is constant up to SFR~300 Msun/yr, and then increases towards higher SFR, suggesting that the ISM obscuration plays a significant role in starburst host galaxies, and (2) at SFR>~300 Msun/yr, the SMGs and IR quasars have similarly compact submillimeter sizes (Re~0.5-3 kpc) and, consequently, the ISM can heavily obscure the quasar, even reaching Compton-thick (N_H>10^24 cm^-2) levels in extreme cases. Based on our results, we infer that ~10-30\% of the IR quasars with SFR>~300 Msun/yr are obscured solely by the ISM.