Why would a President want to hide from eligibility requirements?
If the cops ask to search your car and you refuse are you hiding something or are you demanding your Constitutional rights?
Now if your neighbor demands to search your car are you hiding something or just telling your neighbor to take a hike because he is a nosy jerk just trying to harass you.
Point being that the election process requires that the candidate demonstrate his/her eligibility to the proper authorities, in this case the Sec’s of State in 50 states. Every state, even Palin’s Alaska, placed Obama on the ballot for consideration by the electorate. He won the vote among the populace, in the electoral college and then the election was certified by the elected members of the legislature. Everything was exactly as outlined by the Constitution.
Also, the Constituion allows for only one means by which to remove the president and that is by Impeachment. No other means. Impeachment must be initiated by the Congress and no successful law suit in the courts can compel the Congress to Impeach.