Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
In no other respect is any other single profession granted special protection under the Bill of Rights, so why would anyone try to argue that someone who claims to be a "Member of The Press" gets something special out of the Constitution? Members of the clergy don't claim that they get special legal protections, even if legal precedence has caused the de facto status.
When the Founders first started arguing about the Bill of Rights, it was their intention to protect the freedom to express opinions. There are several different ways to overtly express an explicit idea, but the two main ones were most in need of protection - either through speaking or by writing it down. The new printing press had managed to start giving the colonists a means of expressing ideas to people who might not be present at its conception and evolution (say, around drinks at a tavern one night), and who would come along later to read the broadsheet pinned up in the public square. And it was the freedom of using your speech to express an idea, or to use the [printing] press to express it.
It was all about expressing the idea, not whether the person was paid to express it. Think of the two different levels of damaging another's reputation, slander and libel. The only difference between the two is whether the damaging expression was spoken aloud or written down and handed around. It's the same with the "Freedom of Speech, or of the Press" (which is exactly how it is phrased - see above), and should give a clue to what the Founders meant when they wrote it down the way they did). The lack of a semi-colon shows that it is part of the same clause, and part of the same thought.
Your right to express an idea, and the reach of that expression is entirely dependent upon your assets. If all you have is a soap box on a corner, then the only ones who hear your ideas will be the people who wander by during the length of your speech. If you happen to have access to a TV network or high-volume blog, you can have hundreds of thousands of people, or even possibly millions, (or merely hundreds if you're MSNBC) see what you have to say every day, and that is perfectly legal. You don't have to belong to any kind of specific union to be able to print out something and hand them out on street corners. And you don't have to have a special ID card just because your printing is actually appearing on a laptop monitor in a Starbucks halfway around the world. It is the expression.
So the next time someone starts saying that one must be an accredited journalist to have protection of that Freedom of the Press, let them know the truth.