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Still, Tuesday’s OMB statement was less decisive than its July 18 veto threat against the GOP’s Cut, Cap and Balance Act, which passed the House but stalled in the Senate.

That announcement included a several-paragraph explanation of White House objections to the measure, declaring: “If the president were presented this bill for signature, he would veto it.”

In his Monday speech, Mr. Obama also called for voters to call Congress and demand a compromise, and on Tuesday many responded, overloading the phone lines and shutting down some websites.

Kara Rowland, Paige Winfield Cunningham and Sean Lengell contributed to this article.