Now, in that sense, let's review exactly how "our"[] government measures up: Individual citizens or groups of citizens have minimal means of influencing their own government through the means of the system - i.e. their representatives. Petitions change nothing, letters to representations to MPs / Congresspeople will receive a form reply and will usually be ignored. Occasionally, when public sentiment doesn't conflict too badly with economic interests, minor tweaks can be made, but that's about it.
Where real change has occurred, it has been done so outside* the institutional parameters of the system. The abolition of slavery took a civil war, and the vote for women and civil rights took massive public protests, illegal acts and (in the case of the suffragettes in the UK) hunger strikes.
So yes, change is possible. But it was never achieved within the confines of a system largely designed and evolved (I contend) to limit public participation, and certainly not by online petitions.
[*] Not everyone is from the US, y'know.