The short answer to this question is no, you cannot copyright a phrase for the purpose of legal protection. Copyright laws primarily cover "original works of authorship" that are finalized in fixed form of expression. This can include fixed forms of unique ideas, compositions, plays, novels, song lyrics and so on, but they do not cover individual words, common ideas or short phrases. While the desire to protect a phrase closely associated with a business or an artistic concept may be understandable, US federal copyright laws would not offer much in the way of enforceable protection.
Having said that, there is another way to obtain legal protection for a unique phrase. Individuals and companies can apply for a trademark by going through the US Patents and Trademark Office (USPTO). The USPTO can assign registered trademark status to a short phrase if originality can be satisfactorily proven. For example, the short phrase "Just Do It." followed by a distinctive "swoosh" graphic is a trademark of the Nike company. Another shoe company could not legally use that trademarked phrase in its own advertising or promotional materials.
Some people may want to copyright a phrase intended for use as a bumper sticker slogan or other for-profit venture. The current copyright laws in the United States would automatically assign a copyright to a phrase or title or other unique or original expression. There would be no need to submit the short phrase to the official copyright office, but some people may want to establish the creation date in order to protect themselves from copycats.
There is a good reason why it is nearly impossible to copyright a phrase. Copyright laws are only effective as long as the copyright holder remains diligent about prosecuting violators. If an individual decided to copyright something as simple as "Hello, may I help you?", he or she would shortly be overwhelmed by the number of potential copyright violations. The phrase would be in such common usage that enforcement of a copyright would be virtually impossible.
If the short phrase were trademarked, however, legal enforcement would be much less stressful. Violations of a registered trademark are easier to prove in court, and the phrase is more likely to be unique and original. The word "threepeat" is actually trademarked, for example, although very few people would have an occasion to use it for commercial reasons. The owner of that trademark may decide if any future usage of that unique word is worth the expense of legal trademark enforcement or not.