The only way anyone can ‘conquer’ the Supreme Court is to have at least 3/4 of the states ratify an amendment to the Consitution. Even then, the amendment can be misinterpreted ala the Commerce Clause.....
No. Amending the Constitution is, by its original design, very difficult. That's why Roosevelt, rather than proposing a Constitutional Amendment, sought to solve his "problem" by having Congress pass ordinary legislation permitting a Supreme Court of up to fifteen justices. The number of justices on the Supreme Court is not fixed (currently at nine) by the Constitution, but rather is specified by statute. In fact, the SCOTUS began with only five justices, later increased to seven, and then to nine - all by legislation.
The point is that Obama could legally urge Congress to increase the size of the SCOTUS without the need for a Constitutional amendment. However, with the Congress as it currently is, such a proposal would, thankfully, face certain defeat. So chances are slim that he would repeat Roosevelt's mistake.