Interesting question and the answer below, that I hope is accurate, shows why people need to be careful about this.
The approximately 3% statistic you quote is correct (or, at least, was correct 15 years ago). I can't find a total emissions figure after a fair amount of searching, but in recent years burning of fossil fuels worldwide leads to about 33 billion tonnes of CO2 emission. This does not take into account deforestation, etc.. By comparison, forest fires (assumed natural here) and plant decay produce 440 billion or so tonnes of CO2 annually. So it would appear that the human effect is relatively small -- although there hasn't accounted for all possible processes of CO2 emission.
The point, though, is that plant life, algae etc., also absorb CO2 to the tune of about 450 billion tonnes each year. Now, suddenly, we can see why the human effect, while comparatively small, is tipping the balance. Before we started burning fossil fuels, chopping down trees, etc., the CO2 in/ CO2 out were roughly in balance -- indeed apparently there was a net CO2 loss[i from the atmosphere, by about 10 billion tonnes. Our extra 3% or so has tipped this the other way -- there is a net CO2 [i]increase] of about 10 billion tonnes (on these figures) each year.
In fact the balance is more sensitive than that, as the figures I am quoting omit various sources (both natural and human), and presumably also various absorbers of CO2. But the general point is correct -- that CO2 emissions were previously in a delicate balance. And our extra contribution, even if it is comparatively small, is enough to upset that balance.
Moreover, of course, there are other greenhose gases such as methane, CFCs, etc -- CFCs are completely unnatural, and in the short term are around 11,000 times "better" as a greenhouse gas than the equivalent amount of CO2. Methane, meanwhile, is primarily released from livestock and rice fields and is 25 times "better" than CO2 as a greenhouse gas. In this one our contribution is even more marked -- human or human-related emissions account for well over 50% of annual methane emissions.
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In short: the difference man-made CO2 emissions makes is the difference between 98 and 102 when you want to be less than or equal to 100. Small -- but also huge.