The Speaker of the House has no more responsibility in verifying the eligibility of the POTUS than any other member of Congress. The Speaker has one vote, just as every other Representative or Senator, at the joint session of Congress following the Electoral College vote which certifies the eligibility of the POTUS and results of the election.
Then who does have the responsibility to know if the proposed POTUS has the qualifications to be President before He/She is put on the ballot?
