Unimpressed, the White House issued a veto threat against the bill and Democrats said they would sweep it aside in the Senate.
Obama followed up his public remarks with phone calls to Boehner and the three other top leaders of Congress, telling Republicans he would continue to oppose attempts to delay or cut federal financing of the health care law.
Boehner spokesman Brendan Buck said the House’s top Republican told the president that the health care law was costing jobs and that it was unfair that businesses were getting exemptions but American families were not.
The impact of a shutdown would be felt unevenly.
Many low-to-moderate-income borrowers and first-time homebuyers seeking government-backed mortgages could face delays, and Obama said veterans’ centers would be closed.
About 800,000 federal workers, many already reeling from the effect of automatic budget cuts, would be ordered to report to work Tuesday for about four hours — but only to carry out shutdown-related chores such as changing office voicemail messages and completing time cards.