Boehner announced his resignation on Friday under pressure from conservatives.
McCarthy, who is Boehner's No. 2, sent a letter to GOP lawmakers on Monday pledging to fight for conservative principles - and asking for their support as the next speaker.
The California Republican is strongly favored to get the job though he faces a challenge from Florida Republican Rep. Daniel Webster.
McCarthy is serving his fifth term in Congress and has been endorsed by Boehner.
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