When the resources are available, critical congenital heart diseases (CCHDs) should ideally be detected in utero; however, their later detection at birth can still reduce negative outcomes and risks. This study aimed to assess the extent of cardiac screening implementation in a national sample of hospitals within Mexico’s public health services. A cross-sectional survey was conducted to identify the barriers and facilitators to neonatal screening using a sample of 76 hospitals. The descriptive statistics and associations were analyzed, with significance set at p < 0.05. Only 12% of hospitals reported the routine implementation of CCHD screening, while 20% used variable screening criteria. A potential mandatory implementation of CCHD screening was associated with increased odds of perceiving the lack of protocols and guidelines as a barrier. The most frequently reported obstacles involved a lack of the following: equipment, designated physical space, trained personnel, and adequate training. Nevertheless, the facilitators identified suggest that when combined with standardized guidelines and protocols, routine nationwide implementation may be achievable.