Actually, what's important there is the absence
of forces when you and the spaceship quit touching. If you step outside the ship, you will almost certainly have a slight velocity difference from it. In the absence of any forces, both you and the ship just keep your different initial velocities, and get farther and farther apart. The rope is there to allow you and the ship to exert some force pulling you back together. Gravity between you and the ship does the same thing, but it's too weak to be of much help. A very slight push as you leave the ship will give you enough velocity difference from the ship to never return via gravity.
Actually, while we're on the subject of gravity, let's consider the case in which the space ship is in orbit around the Earth. The Earth's gravity weakens as you go away from the center of the Earth, inversely proportional to the square of the distance. If an astronaut is separated from his spaceship by a tiny distance, then the acceleration due to gravity will be slightly different and they will follow slightly different orbits, drifting apart.
If the astronaut has an initial velocity with respect to his spaceship which points away from the center of the Earth, his new orbit around the Earth will be elliptical with almost the same period, but the radius will oscillate outwards and inwards and back again. But even a small change in the period of the astronaut's orbit will take him far away from his spaceship.
Forces arising from the different strengths of gravity from one place to another are called "tidal" forces, because it is the variation of the sun's and the moon's gravitational fields across the size of the Earth that cause the tides.
These gravitational effects are quite small compared to what velocities can be picked up just by the astronaut stepping away from the spacecraft with some velocity, or by tossing a wrench, say in one direction and recoiling in another.
(republished on 07/11/06)