First of all, President Trump is eligible for the speaker’s position per prior publications. Advertisement - story continues below Need to Relax with a Strategic Game? Escape Reality with This Fun Game. Need to Relax with a Strategic Game? Escape Reality with This Fun Game. …The House can elect whomever it wants to serve as speaker, even if it’s someone who isn’t a member of Congress… …The speaker of the House has always been a member of the House of Representatives, even though the Constitution does not list House membership as a requirement for the job, simply saying lawmakers “shall...