If you have a relatively decent paying job with good opportunities for advancement, combined with a long enough timeline (say, 8 to 10 years), it’s feasible to put away $150K if you limit your spending. Try to live like you did as a college student. Live with roommates, don’t buy a car, cook most of your own meals, don’t spend money drinking in bars/clubs, don’t buy a bunch of expensive shit you don’t need (that includes clothing.)
If you make a $60K salary at age 26, that’s $5000 a month before taxes. Looking on Craigslist, you could get a decent room in the city for about $1200 a month. Figure in another $1200 for food and expenses and that brings you up to $2400 a month. If you look outside the city (East Bay, especially, you can find even better deals.) Certainly, this is a bare-bones budget but if your goal is to sock away money quickly, it will be worth it.
In a few years, your salary will probably go up. Way up, most likely. Keep your living expenses low, though, and you’ll be able to save even more quickly.
You could try investing some of the money. (I can’t tell you how to do that, but it’s possible you can increase your nest egg through wise trades or whatever.)
Also, if it’s possible, you could get a second job or take on freelance work. In my experience, it’s often easier to make extra money than to strictly save what you have. But this may depend on your individual skill set and industry.
I purchased a house in 2007 with an $85K down payment. Nobody chipped in. I didn’t live as austerely as I am recommending for the entire time, but I did for the previous three years (I lived in Seattle, paid only $500 for a room and I did have a car (for which I paid $1200). I didn’t have much of a social life, so that kept expenses low, but when I did go out I didn’t purchase alcoholic beverages (that’s a real budget killer, but it’s easy to have fun without drinking when there are other distractions around you, plus being the designated driver often helped me avoid paying cover charges.)
It can be done, but it takes patience and sacrifice. Rent is your #1 adjustible expense. A car can be expensive, too, as can clothes etc., but you don’t need a car or new clothes all the time to live. Good luck.