post doc research and problem with its progress
Your question is very general and hard to answer. The answer also depends crucially on the kind of post you are applying for. Basically, some postdoc posts are created to support the research proposed by an applicant (i.e. you are a PI on their own project), but many posts are created to support an existing project (you professor is PI and you are Research Assistant/Fellow).


When you are a PI, you can propose any research project that interests you. However, remember to use SMART objectives. If you propose several disconnected research directions, think how realistic is to achieve them in a timeline of your post. Consult more experienced colleagues if needed.
When you are a RF on an existing project, make sure your application relates and reflects the topic and aims of this project. Check PI's bibliography and the information available about this project. 


If you do not think you can make any progress for the chosen topic during the post, it is unlikely you will get any funding for it.