What happens if I only do on-site optimization?

I've done SEO for local businesses and in my experience on-page SEO was enough. On-page is always the first step and will definitely give them better rankings than before. If they're not happy with what on-page alone gives them, then it's time to discuss off-page. If they are, then it's on to the next one.

Backlinks are most useful for global competition, where you have hundreds of sites from all over the world, all with sufficient on-page SEO, trying to rank for the same keywords. When you only have 4 competitors who probably have no idea what SEO is, shit becomes much easier.

It depends on the keywords they are targeting and the competition level in that geo for those kws. At those price points, it is important to convey to the client the value of long tail keywords as that is most likely what you'll be able to get some wins on sans any budget for link building.

Good luck!

You miss 90%.

The BEST is that you don't get any penalties from G.
And the WORST is that you don't get any rankings! ;-)

There are two aspects of SEO first is on page SEO and second is off page SEO. In on page SEO we include meta tags in our website and then google webmaster and analytics. This work is done only one time but in off page SEO we build relation with other websites so off page increased the ranking of your keywords and traffic as well. So off page played and important part without it we can do this rank our keywords.

It is possible to rank with on-page optimization only but you would be able to rank only low competitive keywords... if your site is on EMD and you are targeting keyword on home page and you are creating content regularly, it would work for link building as your site is being updated regularly and it helps rank.