Without Congress, it would take 2/3rds of the states to ratify...That is possible....
Yes, it is possible, but it has never actually been done before. That alone makes it a long shot.
The Constitution provides that an amendment may be proposed either by the Congress with a two-thirds majority vote in both the House of Representatives and the Senate or by a constitutional convention called for by two-thirds of the State legislatures. None of the 27 amendments to the Constitution have been proposed by constitutional convention. Source: Constitutional Amendment Process