Eggs are just for the Whacking Day event. Having Homer do the snake hunt and Lisa do her homework are the quests that will get you to where you can start whacking snakes. Unfortunately, the event is supposed to end sometime tonight. There should be an update in the next few hours that will remove all the whacking day quests ability to get eggs.
Can the game be completed without the expenditure of any real money? Even if it takes “forever”?
I like doughnuts as much as the next guy, but…well, you know.
I haven’t spent any real money on the game and I’m on level 28 (last available level currently) and was able to get all the whacking day prizes (thanks to my SDMB friends). I started playing some time between Halloween and Christmas. However, there are very few available donuts for the cheap among us so the premium characters and buildings are generally out of reach (I did get Squeaky Voice Teen in one of the weekly Mystery boxes).
I still think the game’s a lot of fun, but it can be annoying missing out on some of the donut-required fun (I would really like Doctor Nick). 
I don’t know if we’re friends, but send me a request if not (punkyb1980) and you can see what a donut free town can look like. You need friends to progress in the game, I was kind of late and missed out on some special event prizes because of it.
I am also playing without putting money into it. I have lots of great stuff and am on level 25, I think. I only started playing in February and as an Android user, couldn’t have friends until April. I do kay. It is really fun and you can get there. I have about 40 donuts. I would have more, but I used them in the training stages of the game before I realized how rare they are. Add me as a friend, the name is the same.
It’s Friday and I’m stil whacking snakes. I just sent Homer on another 24 hour snake hunt.
We have an update (level 29) AND AN EXTENSION. Whacking Day now ends on the 16th. Looks like I can pick up a Whack Box or two.
This terrific news! I could make it to the shady motel. woo hoo!
Cool! Back in business!
Do you still want my eggs? I’ve slowed down my whacking now that I have all the stuff and I’m just gathering up whatever comes into my town, so I won’t have as many eggs as I’ve dropped off in the past. But I’m prepared to stand by my prior commitment.
For myself, I don’t need any eggs. I’m nearly to my first whack box and anything else I get is gravy.
An extension? In that case, egg me! I’m at just over 8k, maybe I can get the next prize!
I’m in the same boat as Antigen and at about the same number of snakes, so I’ll happily take extras too. 
Where did you hear about the extension?
I also got the level 29 update and still have snakes.
Tap the little question mark next to your snake and egg counter. This brings up the Whacking Guide. At the bottom it used to say: “The event ends May 9 2013”. The date is now changed to the 16th.
I’m at the highest level without spending a dime. Started after Christmas. I wouldn’t spend donuts on speeding up tasks, they’ll finish eventually.
I’m less than 500 snakes shy of the second prize box – I should reach that in the next day or so. If this goes another week then I might even make it to the fourth box.
That would be awesome, thank you!
OK, but I hope your town can handle it. I might be dropping off upwards of 75 eggs a day!!
Did they add anything prize-wise after the Motel (besides whacking boxes)?
Nothing new for Whacking Day. But the level 29 upgrade includes a bunch of neat stuff. Skinner’s house with Agnes Skinner. A park entrance decoration. A new wall type. Sprawl-Mart as a premium building. And an open-air stage premium building where you can send characters to perform.
That sounds cool.
EA should create a task that would make all the Springfield residents riot. Maybe against Homer.