Extension domain name .deals has the possibility to rank but this will depend on the whole domain optimization process to be assisted by the search engine's guidelines and most importantly the users intent for your site pages that will be provided.
No reason it shouldn't - just follow the rules (unique content, well delivered, links etc) and you'll be fine.
Actually it is not easy. However definitely possible to rank the domain if optimized well. You need to understand it is a continuous process and if you have the patience along with correct SEO techniques, the website can surely rank. Experience in SEO will definitely help you to achieve the goal quickly that you are seeking for.