San Francisco has a population density of 18,451/sq mi (7,124/km2)[1]. In the Unites States, That is denser than just about any place other than Manhattan. At peak times, busses are crowded and traffic sucks. Personally speaking as an SF resident, having more efficient public transit options would be awesome. I'll let others crunch the numbers of the feasibility of building & paying for it.
> In the Unites States, That is denser than just about any place other than Manhattan.
I think that depends on your definition of "just about." Every borough in NYC aside from Staten Island is much denser than San Francisco. Additionally, many parts of where I'm from – northern NJ – are even more so: Hoboken, West New York, Union City (the densest city in the country), Guttenberg (the densest township in the country), and more.
If you're talking about cities larger than a certain size, then perhaps, but even then, I personally think it's a bit misleading to single out just Manhattan.
It is not a matter of feasibility. Infrastructure transit produces tremendous returns in productivity. Even insanely overbudget projects like the Big Dig in Boston are already breaking even after only a decade, because of how much room for growth they produce.
This is why having fast rail, uncongested highways, and always expanding to meet demand are always worth the cost. Unless you can accurately forecast a downturn in regional economic growth irrespective of whether or not you meet transit demands, it is never rational from the perspective of long term city planning for maximum economic throughput to not grow the system and increase density.
Even as someone who lived on the periphery of Boston for much of the Big Dig, it's good that it was done--in spite of all the well-publicized problems. Of course, the fact that Tip O'Neill managed to funnel $10 billion or so of federal money to the city for the project doesn't hurt.
[1] https://en.wikipedia.org/wiki/San_Francisco