If it were me, I'd be digging out my original mortgage contract and deeds and scrutinising the small print to see if there were a clause making me responsible for the pavement outside - and checking where the edges of my plot of land were. And if neither of them backed up the association's position, I should be considering taking all the paperwork to a solicitor and asking what they thought about it. Of course, if there is a clause in the contract that supports the association, or if the boundary has been drawn so that the pavement is actually part of your property you haven't a leg to stand on. The only thing you'd be able to argue is that if they do it without consulting you and it happens to be a month when you can't absorb the expense, and they get it done without sending you an estimate for the work so you can budget for it, that's rather unreasonable.
The flip side, of course, is that your taxes would go up if the state had to do it. One way or another you'd pay for it... and the city council are responsible for the pavements and roads where I live and the one I live on is horrendous but hasn't been touched by the council in over 20 years because they say they can't afford it, even though taxes are exorbitant. I don't know which situation is worse!