Well, they kinda have. With a predicted 60-100 labour MP's in favour, the DUP in favour, likely the LibDems in favour and maybe just 10 Tory rebels, that's a pretty whacking majority.
The public is very much in favour as well, for right or wrong.
Do you have proof of that because most people I've spoken to are NOT in favour? I'm certainly not. In fact I share @Fivering's views. We went into Iraq and Afghanistan without any kind of strategy, including an exit one, and look what happened.
Cameron's strategy is risky, but it is at least coherent. It's also worth remembering that Cameron doesn't have to call a vote - as PM he's entitled to act without a vote.
So why is he bothering to have a vote? Presumably so's he can save his miserable skin when things go pear-shaped, which almost inevitably they will. I don't trust Cameron because I don't trust his judgement, particularly when it comes to foreign affairs, and I find his gung-ho attitude towards all this scary.