US Constitution Series, Article II, Section 4

Article II. EXECUTIVE DEPARTMENT

§ 4. Impeachment

The President, Vice President and all Civil Officers of the United States, shall be removed from Office on Impeachment for and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.

It seems to me that the bar is pretty high to justify removal from office. Of course, the Senate must agree to convict on the impeachment by a two-thirds vote and there is no provisions for appeal to the Supreme Court.

Failure to keep the oath of office by itself is not grounds for impeachment.