First, let's note that by trying to diminish the US role regarding CO2, they're implicitly admitting that CO2 matters. I suspect they know that, but have to then dismiss it (viz. lie) for the sake of their audience.
The fact is, the US has emitted more CO2 than any other nation, by a factor of over two. And that emitted CO2 is just as much of a factor as are today's emissions -- in fact, they're more, since CO2's forcing changes slower than linearly with concentration. For example, the atmosphere now has 45% more CO2 (406 ppm on an annualized basis, as of October) than in pre-industrial times (280 ppm), but CO2's radiative forcing is 54% of its value when doubled.
Here are the data, from WRI's CAIT database (which seems to be offline at the moment). Through 2014:
As you can see, the US has emitted over twice as much CO2 as has China, and almost nine times more than India.
And you can barely detect any US reductions, there near the end of its line.
Here's another way of looking at it: the top 10 cumulative emitters, and how they compare to the US:
This can be broken down even further, per capita, which Damon Matthews et al did a few years ago:
By my estimation, China's cumulative emissions by 2014 were 1.9 times its cumulative emissions of 2005; the US's were 1.16. I haven't worked out the updated numbers for this chart, but there's no way China's per capita cumulative emissions today are anywhere near the US's.