We report X-ray constraints for 20 of 52 high-z ULIRGs identified in the Spitzer xFLS to constrain their obscuration. Notably, decomposition of Spitzer-IRS spectra for the 52 objects already indicates that most are weak-PAH ULIRGs dominated by hot-dust continua, characteristic of AGN. Given their redshifts, they have AGN bolometric luminosities of ~1e45-1e47 erg/s comparable to powerful QSOs. This, coupled with their high IR-to-optical ratios and often significant silicate absorption, strongly argues in favor of these mid-IR objects being heavily obscured QSOs. At X-ray energies, we marginally detect two ULIRGs, while the rest have only upper limits. Using the IRS-derived 5.8um AGN continuum luminosity as a proxy for the expected X-ray luminosities, we find that all of the observed sources must individually be highly obscured, while X-ray stacking limits on the undetected sources suggest that the majority, if not all, are likely to be at least mildly Compton-thick (NH>1e24 cm-2). With a space density of ~1.4e-7 Mpc-3 at z~2, such objects imply a lower limit on the obscured AGN fraction (i.e., the ratio of AGN above and below NH=1e22 cm-2) of >~1.7:1 even among luminous QSOs. Our findings, which are based on extensive multi-wavelength constraints including Spitzer IRS spectra, should aid in the interpretation of similar objects from larger or deeper mid-IR surveys, where considerable uncertainty about the source properties remains and comparable follow-up is not yet feasible.