Deem means to think of something in a particular way, to believe, to consider something to be true. http://learnersdictionary.com/definition/deem The first sentence is incorrect because of the modal verb "should". You already have the verb "deem" and you can't use both verbs in the same sentence. 'Deem' is used differently in a sentence like this than 'think' is. Here are some ways to correct that sentence. I deem Mark unable to pass the exam because he doesn't study enough. I think Mark should study more if he wants to pass the exam. Mark should study more if he wants to pass the exam.

The verb "deem" means "to hold as an opinion; think; regard", so the second sentence is correct, because the president is expressing an opinion of the proposal, but the first sentence is not. You may be confusing "deem" in the first sentence with "decree", which means "to command, ordain, or decide by decree" (i.e. 'I decree that Mark should study more if he wants to pass the exam.')

Deem does mean 'think/believe', but more in the sense of 'express that thought/belief', and only in a formal/official context, or occasionally in a joking pseudo-official context. That is why the second version works, and the first doesn't. I don't think anyone would say 'I deem' seriously, as that would sound very arrogant and pretentious.