Conservative party members were refusing to fall in line behind Ryan, the 2012 Republican vice presidential candidate, after he said he would run under certain conditions to replace Boehner.
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After a closed meeting of House Republicans, Boehner told reporters he supported Ryan to be the next speaker.
The struggle ensued as deadlines fast approached for Congress to act on critical debt and budget issues, with U.S. Treasury Secretary Jack Lew saying he feared a fiscal policy “accident” on Capitol Hill.