With regard to Barack Obama, several courts ruled that they would have entertained questions of his eligibility while he was a candidate but not after he received a majority of the votes of the Electors and was sworn in to office.
“There may very well be a legitimate role for the judiciary to interpret whether the natural born citizen requirement has been satisfied in the case of a presidential candidate who has not already won the election and taken office. However, on the day that President Obama took the presidential oath and was sworn in, he became President of the United States. Any removal of him from the presidency must be accomplished through the Constitutions mechanisms for the removal of a President, either through impeachment or the succession process set forth in the Twenty-Fifth Amendment. Plaintiffs attempt to subvert this grant of power to Congress by convincing the Court that it should disregard the constitutional procedures in place for the removal of a sitting president.
The process for removal of a sitting president— removal for any reason, is within the province of the Congress, not the Courts.
Barnett, Keyes et. al. v Obama, et. al. Judge David O. Carter, U.S. District Court for the Central District of California, 10/29/09
Also most of the states have election laws that permit opposing candidates to challenge the credentials of other candidates but McCain, Palin, Romney and Ryan did not challenge Obama and neither did the Republican Party or any other political party.
I just cannot imagine the judiciary exposing itself to all of the crazy claims that will result from a willingness to become a screening committee for presidential candidates. They have read all of the background that everyone has now read. They know that there is no clear answer and that there is no way to avoid looking like the court is just making up standards on a case by case basis. And, they know that they will never satisfy the true believers because the court will no doubt be utilizing fraudulent documents from government agencies, stuff like birth certificates, etc. ;-)
FYI
Cruz’s response to ballot challenge
http://sos.nh.gov/WorkArea/DownloadAsset.aspx?id=8589951054
Rubio’s response,
http://sos.nh.gov/WorkArea/DownloadAsset.aspx?id=8589951072
Other related documents
http://sos.nh.gov/2015-16BLC.aspx