Starcraft 2 Zerg – Why is Zerg Behind Without 1 More Base?

You don't need much base defense. Try getting by without building any bunkers, and just defending early with the marines that you build, and later with tanks. You'll definitely need a good wall-off and units correctly positioned on the cliff to do damage to the zerg as the come around the corner. You can afford to expand pretty late (you only need it for the gas), once you have the majority of your tanks sieged on your cliff. Expanding late will allow you to not have to spend any extra money on base defense.

You should not stop producing SCVs for a very long time. It should be at least 10 minutes where your command center is NEVER idle. Get an orbital command as soon as your first barracks finishes, and use MULEs every time its up. Pump marines non-stop from your first barracks (no add-on). As gas allows, get your factory up and pump tanks until you hit 8. Get siege when you have enough gas to research it without stopping tank production. As your 1-base economy starts to peak, you will have enough extra minerals that you can't spend with your limited number of production buildings. At this point, build a second barracks and you'll soon be at 30 marines. Once at 30, put tech labs on your barracks and get ghosts as gas allows. You should also have extra minerals, since 2-rax marine, SCVs, and a factory should not be spending it all. When you have 400, build a command center inside your base (you'll float it down when its done). Move SCVs down from your main, and prioritize gas. You should be close to 8 tanks by now, so put all your gas into ghosts. If you can't spend all your gas on 2 rax ghosts, get more.

I got gold on this challenge on my first try. It shouldn't be too difficult if you follow good macro fundamentals (constant production, don't supply block yourself, correctly prioritize your resources).

The effect is mostly that you earn less resources, which means that you can not expand at the same time as the enemy and you can only produce workers at a slower pace unless you accept falling behind in unit numbers.

You can recover from an early worker disadvantage by either killing a lot of his units and then expanding and getting a lot of workers while he rebuilds his army (especially true for zerg) or by killing enemy workers with drops while you have a similar sized army.

If you fail to do either then you will slowly fall behind because you always have less resources and less units than the enemy while the enemy economy is increasing faster than yours, just because he can afford to spend more resources on it instead of on unit production.

Simplified Math:
1 Worker gathers 0.7 minerals per second (according to this Teamliquid Thread).
This means a single worker gathers the resources required for 1 Marine every 70 seconds.
So being one worker behind doesn't have an effect immedatly, but after those 70 seconds you will be one marine behind unless you skip a worker and instead produce an additional marine, which would put you another worker behind, resulting in being behind a marine every 35 seconds unless you skip another worker. Continue until you are dead.