Upvote:2
The list of TSA-accepted ID includes "Border crossing card," so that should be considered acceptable for airport security purposes.
However, keep in mind that you can't use the card alone to cross the border by air, so that will limit your travel options and prevent you from flying back to Mexico if a family emergency or something requires a quick trip home. Unlike a passport, it's also not an incredibly widely known form of ID in the US, so hotels and other businesses that require ID may not be willing to accept it, especially away from the border. You could contact them in advance if you're not sure it will be accepted.