For all the people who have insurance today, how many do you think love to go to the doctor at the drop of a hat?
Many of the Republicans make it the party of exclusion -- the party of the rotten apple that kills it for everyone else. They would rather see 9 loved ones shot in friendly fire on the chance that a 10th person who invades their home might be a bad guy who eats the lead of the Second Amendment. Similarly, they would prefer to deny reasonable coverage to 9 needy, wage-earning people for the prospect of not paying for the one dirt-bag low-life who does little to deserve his coverage.
Yes, most folks don't need specialists as much as general care. But the more general care, theoretically the less specialists you need to see. Right now, the uninsured are seeing a lot of specialists, and the people with insurance today are effectively paying for that to keep hospitals solvent. If you can shift that expensive specialist care to more cost-effective preventative care, while keeping said hospitals solvent, that's a financial win.
As for overall premiums rising, implementation is the key. If screwed up (not hard to expect, given this administration), they could go up. But a reasonable administrator should be able to make this a net lowering of premiums. Maybe the Obama administration won't see the savings, but some future president should be able to.