The cheapest way to have a baby? Move to a small town in Canada, and give birth to a baby who is the first grandchild to your in-laws, and the first girl grandchild on your side of the family. 
We have government health insurance (free or almost free) plus we are covered for extra stuff (e.g. prescriptions) by our health plan through work, for which we pay a small monthly fee.
We saved a lot of money by not having a theme for the baby’s room - we painted it a gender-neutral colour, that’s it. We didn’t bother buying a change table or a baby dresser, we just used a long, low “grown-up’s” dresser which we already owned.
Cloth diapers are a saving, but more expensive at first. We use disposables, bought at Costco. She is 9 months old and we probably change her 5-6 times a day. Not necessarily because she needs it, it’s just easier than dealing with a diaper rash! She is still mostly breastfed, with some formula - we buy it at Costco as well. I make most of her food, which save a bit of money too I think.
We didn’t skimp on her carseat or stroller or crib, but we didn’t buy “name” brands.
A lot of her clothes were gifts, or second-hand loans, or bought at Walmart. Although I love a lot of the name-brand stuff, it’s not a priority for us, money-wise. Most of her toys are new, but they also usually only cost between $3 and $20, and she doesn’t have a ton.
Here you get 50 weeks of paid maternity leave from the government - I believe it is 55% of your normal salary. Plus some employers top that up for at least part of your leave. And having 50 weeks of leave, means no daycare costs until your baby is almost 1 year old.
We asked for money for her RESP (post-secondary savings) for Christmas, rather than a bunch of gifts - our baby was born in October, so by Christmastime she was still so young and tiny, she didn’t need much. This gave a nice little kickstart to her savings, which means we don’t have to contribute much each month.
So … she’s 9 months old, and I would guess we’ve spent about $30 / month on diapers, $20 / month on formula (she only has one bottle of formula per day), $20 per month on produce for homemade baby food, $10 per month on baby cereal, $30 / month on baby clothes (undershirts etc - she is growing like a weed!) and say $15 / month on miscelleous stuff (a wading pool one month, a couple of bibs and sippy cups another month, etc.).
$125 / month x 9 months (to keep it simple) = $1125. Xmas presents, some books, mobiles, etc = $500 in total. Stroller/car seat combo and a big-girl carseat (sold to us by a friend who used it once for a grandkid) = $300. So just under $2000.
Dr Phil is on crack.

We used a fairly neutral green, figuring that we’ll change when the kids are old enough to be involved in picking a color. We did use some winnie-the-pooh decals to spruce things up a bit though. I guess we were a bit off, we used a used microwave stand for a change table.