While there are laws and executive orders curtailing the power of the presidency, Obama wields a lot of power. The years of George W. Bush have shown that drastic measures can be taken when there is a treat against American national security. However, I don't think that is a power Obama would be exercising all that often or all that soon.
Any president who wishes to have this power, should be a given a vote on it, but only if he forfeits his secret service protection in return. It is only fair. We are not going to let him or her have all this power with no repercussions. We're not going to play this little game. We'll see how long it lasts.
No man in this world should be given the power to kill whomever he wants as long as he THINKS they are involved with a terrorist association. The Seventh Amendment clearly states all Citizens have the right to go to trial, if a person, the president thinks is involved with a terrorist group, isn`t showing immediate threat the president or any other person has no right to end their life. I think Obama wants too much power for himself but hopefully he won`t get it.
He would receive extreme backlash from even his own party, and the uproar in America would likely see an impeachment trial of Obama. That being said, Obama is a fair-handed, logical thinker and would never do something so drastic and idiotic as killing an American citizen on American soil for any reason.
Can the president give an order to kill citizens of the United States within the border without a trial? Yes, but legally he should not be allowed to do so. Such an order violates due process as all of the United States' citizens are entitled to a fair trial under the law.