Yes, voters do have influence in general elections. However, they need to be informed voters that will hold politicians accountable. Many voters simply vote based on their party affiliation; often leaving incompetent politicians in office for years. Informed voters, however, could influence general elections if they stuck together to hold elected officials accountable.
When the New Zealand Prime Minister called the general election of 1984, he was drunk. This does not prove that voters have no power - indeed, it confirms the opposite. Voters are always able to exercise their opinions about who they think should hold power, regardless of whether or not their leader has had a little too much to drink.
It would be nice to see a popular vote election back in place. right now our voting process in the US is useless. It puts people into power based on the dollar value of their constituents. What can you do for me if I get you elected? Would a general election fix that? I don't know, but I doubt it could make it any worse!
Honestly, voters do not have much of an influence in any election. If people could really change things by voting, they would not be allowed to vote. It is just a process that makes people feel like their voice and opinions actually matter to those in charge. Newsflash! They don't!