By Andrew Chung and John Kruzel WASHINGTON, April 2 (Reuters) – President Donald Trump took the short trip from the White House to the U.S. Supreme ⁠Court ⁠with his signature priority of cracking down on immigration largely intact, given repeated ⁠interventions by the nation’s highest judicial body in his favor. By the time he left, his luck may have run out.  With Trump looking on from the public section of the courtroom – ​a historic first for a sitting president – most of the nine justices seemed unwilling on Wednesday to let him proceed with what may be the most audacious piece of his restrictive immigration agenda. At issue during the arguments was his executive order that would deny birthright citizenship to hundreds ‌of thousands of babies born each year on U.S. soil. The members of ‌the court, led for more than two decades by conservative Chief Justice John Roberts, signaled that the administration’s arguments backing Trump’s effort are legally invalid and inherently impractical.  “I do not think that Chief Justice Roberts wants to go …