The House can impeach on a simple majority. Impeachment is like an indictment in criminal law. It refers the matter to the Senate where a trial is held. In the case of Presidential impeachment proceedings the Chief Justice presides. The Senate must have a 2/3 majority voting guilty to convict the President. The Senate can then remove the President from office, and can impose a further penalty barring the convicted President from holding federal office in the future. That is the limit of its jurisdiction - it could not, for example, sentence the President to prison.