This may sound too simple but have you tried opening a free online-only savings account and then auto-transfer over what you can afford to save each time your paycheck is deposited into your primary checking account?
If all you see is what's left over (in your primary checking) you won't be spending it. Just don't log in to the savings account and transfer it back. 
@Anonymous wrote:hey that should be easy peasy for you. i am now well off but used to make 36k on a s#ity job and was able to save 25k easy each year. paid cash for both my house and car and continued to save(even easier after buying a house cos my housing expenses were minimal) until i reached another 100k in savings. in total i worked for 7 years(making about35k) and ended up with a paid of house, new paid off car and 100k in a bank.
i always read these stories about people making 65k or even 100k and struggling....i and i just dont get it.
it is very simple. make a budget and dont buy crap. especially dont buy crap on credit and pay intrest.
after i bought my house i literraly lived on 6k/year. so in your case save 20 easy and live like a king for 27k for just one year and you will have your 20k saved.
all this changes a little bit if you have kids or some other stuff but basic thing is the same. make a budget and stick to it. very simple.
While I get your point and agree with ability to save, you can't really say you don't understand how people can't afford to live on $60k a year.... well it mostly has to do with the cost of living in your area. There are many parts of the country where you could literally not even rent a shed if you are making only $35k a year, much less have money to buy a car and save.
$60k a year is nothing if median home prices are over half a million dollars.
As for the OP one great avenue I found for saving money is to use a service like Acorns. You can set a weekly or monthly transfer and can even have it round up and deposit the "change" from purchases when you swipe your card. You then set rules for your profile about risk and stuff like that but they basically invest the money for you in various ways depending on how you answer the questions.
Benefits of this is you will get a much better return than just having the money in a savings account, and also if you want the money back it takes usually over a week to get it because they sell of your investments blah blah then transfer you the money. This means if there was an emergency you certainly could get the funds back, but it's not easy. Also you don't have any type of card, or checks, or ATM access to that money so.... works for your "hard but not impossible" to get strategy.
