No, a few billion. The red giant lifetime of a solar mass star is very short compared to its main sequence lifetime, typically a few million years compared to ~10 billion years of main sequence lifetime.
What happens when the sun goes into the red giant phase is that the hydrogen that has fueled the sun's fusion reactions in its core is used up. This means that the radiation pressure that counteracts the gravity is lost and the core will contract. The contraction of the core will heat it up immensely. This enables hydrogen fusion in a shell at the edges of the core with insane reaction rates, since the temperature is now much higher. This, in turn, means that the sun's energy output is increased roughly a thousand to ten thousand-fold. This expands the sun's outer atmosphere greatly due to increased radiation pressure from the core and we've gotten a red giant.
The thing that ends this is that the core once again runs out of hydrogen and heats up even more due to compression. It will, however, at some point run into electron degeneracy pressure (yay! Quantum mechanics!) which means that it cannot contract any more but will continue to heat up due to material being piled on from outside. When heated to a high enough temperature (~100 million kelvin) the entire core will instantly start fusing helium and throw off the outer atmosphere (which is at this point reaches roughly to the orbit of the Earth). The sun will then fuse all helium available to it and end its life as a slowly cooling white dwarf since temperatures will never reach high enough to fuse heavier elements.
Wow, that turned out a lot longer than expected. One wonders at what one can accomplish while bored needing to write project reports. But hey, free fresh-up on stellar evolution!