How many people opt for it would depend primarily on 1. how much cheaper it is, and 2. how different the benefits are from the competing private options. If cost were the only consideration in making purchases, Yugo would be the world's dominant car company.
Also consider the various restrictions that have been floated on who would qualify for the public option. Its earliest incarnation was a free-for-all, but to make it more politically palatable, entry may be limited based on employment and/or existing coverage and/or income level.
In another thread I suggested you read
this PNHP article which bemoans how toothless the public option is (from the perspective of single payer advocates, that is). The currently debated notion of a public option originated from a man named Jacob Hacker in 2001, while he was still in graduate school. The Lewin Group analyzed his methods and estimated that 113 million (46% of the non-elderly) would enroll in an open public option run through Medicare's infrastructure, and that the uninsured would drop to 5 million.
Now, compare that figure to what is coming out of the CBO with the public option proposals
as they have thus far been written: the so-called tri-committee bill is projected to enroll 10 million, and the Senate HELP bill would not be able to set premiums lower than the private options.
Feel better?