Dream job, or current job?

If you really like the company that made you the offer, I'd recommend looking into how often their contractors are hired and in what time frame. Where I work it is the norm that contractors are hired to full time positions after the trial period. On our 20-person team, around a quarter have been hired after a contractor-to-hire period in just the last 8-10 months (The rest were brought in as full time employees). However, every company is not going to be the same. Either way, I'd suggest finding what else is out there (if you haven't already). If you're considering leaving your job it would be good to apply to various other places. Even if nothing comes of it right away you can continue to build your portfolio and look for the right offer. Good luck!

Take the leap of faith 100% or you will be stuck in your current job forever.

Chris, that can be quite the dilemma, and honestly I don't think there is a good answer. If you were young and single I would say throw caution to the wind. If things didn't work out it would be easier for you to recover. However, given that you do have a family and financial responsibilities there is a lot for you to consider. An additional $20,000 a year can seem pretty tempting, but as a 1099/contract employee you incur additional expenses. You will be paying both halves of your Social Security tax, meaning you can add roughly another 15% to your tax liability for the year. Also, health coverage comes into play. Since you live in the US you will eventually be required to have health insurance for your family, but you should maintain health insurance regardless of the law since medical expenses are the number 1 reason bankruptcy in the US. Paying taxes at the end of the year can be more expensive if you have a lot of deduction. My recommendation is to look into the addition costs of being a contractor and your personal finances, then see if the numbers work for you. Personally, I think that $20,000 will be spent on business expenses and not on personal items.

Whatever the case may be, don't be discouraged if you can't take the job. If you really want to work in the web industry, then take your time and build towards that goal. You could try doing some small gigs and built up experience and a portfolio. If you've already done that, then keep looking for the job that works best for you.

Would like to thank everyone for their response, and Ashley you are right. The one thing that I have always told myself is that I don't want to ever regret not doing anything in my life and I know that in 10 years I will regret nit taking this leap. Tanking what everyone said to heart, the job may last and it may not, I will prepair (save money) for the worst and give it my best.

I would recommend always following the path that has the most challenge and growth opportunity (which only you can define, according to your goals). You're never going to regret trying something new that will help you build new skills - I'm sure it will open new doors in the future.