'Grammar' may be useful for all sorts of things but it may or may not help you understand why things are being said or written.
Consider, 'We must live within our means' as repeated by representatives of the government.
If we inspect that sentence according to the standard 'grammar' that I was taught we discover that this is a 'sentence' and the kind of 'sentence' that is a 'statement' (not a question or a command) It's a sentence partly because it begins with a capital letter and, given that it's a statement, we say this because it contains a 'finite' verb that has going along with it all that you would expect it to - a 'subject' and an 'object' if the verb 'needs' it. It's complete.
The subject of this sentence is 'we'. The verb is made up of two elements 'must' and 'live'. The terminology tells us that 'must' belongs to a family called 'auxiliaries' and within that family there are some specific kinds called 'modals'. The word 'live' in this sentence is a 'main verb' and it's the kind that is 'active', 'present' 'intransitive' - it doesn't take an object. The phrase 'within our means' seems to modify the verb 'live' or 'must live'. So it's called 'adverbial' an 'adverbial phrase', made up of a preposition 'within' and a 'nominal phrase', 'our means', which in turn is made up of a 'noun' 'means' and a word that describes it which may be described as a 'possessive adjective', a 'possessive' or, as some Americans tend to call it a 'possessive pronoun'. Further descriptions, 'we' is a 'possessive pronoun' of the kind that is described as 'first person plural'.
(If I've got any of this 'wrong' it's because years and years of grammar teaching didn't sink in, or I am just not good enough at it, even though I was 'taught'.)
I haven't given much explanation for the above - sorry but this is not the point of this blog.
My point is, what does this grammar tell us about the purpose and meaning of this sentence?
My view is: not a lot.
The people inventing it and repeating it have used all the words 'correctly'. It doesn't say for example "I must to live within our means'. Or 'I musts live within our mean'. (And you can have plenty of fun thinking up some more.)
Now let's examine 'we'. 'We' in this context means 'all of us in the UK'. But how are these 'means' distributed? And do we all 'live within' them in the same way? In fact, some people have to live within very small means, some live within means that are huge. However, those who will be on the receiving end of living with less will be 'living within' in a very different way from those living within a huge surplus.
So 'we' is in fact a deceit. It makes out that 'we' are in the same boat all facing the same dilemma, while concealing a vast stash of wealth that is not part of the description 'means'.
I'm going to suggest that none of this is apparent through old-fashioned grammar analysis. It needs another kind of analysis, a combination of semiology and ideological analysis available to a combination of people: ordinary folk with no linguistic training of any kind who can spot the bullshit, and know straightaway that someone is using a common phrase in order to trick them; people who do know the tools of semiology and lit crit and ideology to get behind this sort of thing.