I have to agree with AgentZigzag, two weeks ago the relationship was good enough for you to propose marriage and because your proposal was declined you're embarrassed and talking about ending the relationship. You're upset, in the circumstances thats understandable but take a breath.
Is being married a deal breaker? It sounds like marriage was something you aspired to but obviously wasn't a deal breaker, as you have been together seven years and have two children.
What has reignited the current desire to get married? Your OP gives the impression that your current motivation for marriage is seeking reassurance, you may have doubts about his love and commitment and him wanting to marry you would prove this to you. If you have doubts about his love and commitment proposing marriage was never a good way to allay those fears. Whatever the deficiencies in your relationship are, getting married could never fix them.
He should never have given you the impression that marriage was in your shared future if he didn't want to get married and you should never have stayed this long and had two children if this was so important to you.
Marriage is a personal concept, its symbolism isn't universal to us all. Its aspirational but in reality, it doesn't symbolise forever simply because 1 in 4 end in divorce. So many people are focussed on the romance and the big day that they ignore the contractual side of things and only really understand the details of said contract when they embark upon its dissolution.
He handled it badly and should been more tactful but sounds like he panicked and ran away. Once you have calmed down and examined and understand why you want to get married you need to have a conversation. In the end this could be a good thing, if it brings some uncomfortable relationship truths into the light.
Good luck