There is no technical reason why she could not become president. There is a precedent: in 1916, Charles Evans Hughes resigned as an associate justice of the SCOTUS to run as the Republican nominee for the presidency, losing to Woodrow Wilson in a close race. He was a favourite for the nomination in 1920, when the Republican ticket won by a landslide, but withheld his candidacy following the death of his daughter. However, he did accept the position of US secretary of state in the Cabinet of Warren Harding. By coincidence, Harding also appointed former president William Howard Taft as chief justice of the United States. In 1930, Hughes returned to the SCOTUS as chief justice.
Indeed, while I believe that Hughes is the only person to have served two terms on the SCOTUS, he is by no means the only person to have resigned from the court in order to pursue, or resume, a political career. James F. Byrnes, for example, resigned from the US Senate to become an associate justice of the SCOTUS, only to resign from the SCOTUS after little more than a year to become director of the Office of Economic Stabilization (he later became US secretary of state and governor of South Carolina).