They did. They drafted Articles of Impeachment against Obama, Article 1 was about forged identity documents.
Unfortunately their efforts fell on deaf ears, no one in Congress took up the issue.
Our founders prove more prescient every day, it seems. They wisely foresaw the probability of other nations attempting to take the POTUS position for the purposes of these nations behind the ruse. They tried their best to ensure that they would weed out all but the totally faithful patriots for the job of POTUS. And it has worked. WE are the ones who have failed the Founders. Voters are the ones who failed to uphold the Founders' vision to select as POTUS ONLY those with allegiance to the USA, which could not be guaranteed, but requiring that person to be born on US soil, and requiring his parents to be Americans, was as close as you could get.