Obama had no excuse not to turn over his birth certificate immediately. This is a one page document issued at birth - real simple. UNLESS, You are one of those unlucky one's like me. I never actually needed mine till I was 62 then I could not get it because my just NOT so wonderful mother lied to me my entire life and never told me what my true birth name was. It took us 3 months of guessing games to figure out who I really was. Then we found my birth certificate.
NOW, for Trump's tax return that could be a very complicated issue. The man has many business ventures. Personal tax returns are due April 15th, as long as you have the taxes paid by the 4/15th deadline you may file for 3 month extention to file. This very well maybe necessary for someone in his position, as I have seen it done many times because some of the business ventures maybe partnerships. The partnership tax returns must be completed before Trump can complete his. BUT if the partnership files for an extension that delays the partnership's return and further delays Trump's return. Once Trump's return is filed it maybe subject to audit and if that is the case then he would not be willing to release it to the public until the matter is resolved. There are some clients it actually takes up to two to three years to finalize a tax return with the IRS and God forbid there is a nightmare return you don't even want to know how long and how many days in court it takes before that will get resolved. The US tax code is a nightmare - I hate it!! It needs to be revamped probably put through a shredder!! Although I am very capable of doing my own tax return, I pay someone $375 each year to do it for me just so that there signature is on that line that says prepared by. Because I do not play with the big boys.
I hope that resolves your questions.