WASHINGTON — House GOP leaders Wednesday halted debate on an austere measure that was full of cuts to transportation and housing programs and community development grants, a setback for their budget strategy of embracing the stark spending levels dictated by automatic spending cuts known as sequestration.

GOP aides said there wasn’t enough time in a busy House floor schedule to continue debate, but House Appropriations Committee Chairman Harold Rogers, R-Ky., said it was apparent there weren’t the votes to pass the bill.

As the House measure faltered, a companion bill in the Senate seemed likely to be killed by a GOP filibuster on Thursday for the opposite reason. It breaks the budget limits of sequestration, the automatic cuts required by Washington’s failure to strike a bipartisan budget deal.

Cuts in the House transportation measure were made deeper by a Republican move to cut an additional $40 billion from domestic programs and transfer the money to the Pentagon. That left the transportation measure $10 billion, or about 18 percent, below the Senate’s bill.

Rogers, who often is cautious in his public statements, issued an unusually harsh blast, saying halting debate on the measure reflected a failure of Republicans to follow up on their promises to cut spending with binding legislation.

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