As always the devil is in the details, and I'm old enough I was around and paying attention for the Bush years. The debt limit fight referenced in the essay was actually extremely minor - there was never a real risk of a shutdown, unlike 1995, 2011, and 2013 - and the Democrats' position was broadly not "don't raise it" but "if you're gonna raise it, how about also we fund something other than wars". It's not at all comparable to the times the Republicans have a) actually precipitated or enacted crisis, sometimes with no specific demands, and b) when they do have demands, it's a hard line of tax cuts plus lower expenditures.
Your bias is showing here. Someone could easily come in and say that the Republicans weren't saying "don't raise it" they were saying "if you're gonna raise it, how about we give people some tax cuts too?" And those Republicans really meant it, too (/s)! It's not magically better or less of a political play when the side you like does it, even though Democrats generally cave on their own threats too early.