WASHINGTON — In an effort to put pressure on Congressional Republicans, the White House warned on Sunday that automatic budget cuts scheduled to take effect this week would have a devastating impact on programs for people of all ages in every state.

Cabinet officers sounded the alarm on television talk shows, and their concerns resonated with state officials, who were in town for the winter meeting of the National Governors Association.

Daniel I. Werfel, the controller of President Obama’s budget office, held an unusual Sunday briefing to catalog the effects of the cuts state by state.