This is classic logical fallacy:
“Chris, bless your heart, but not funding the government is part of funding it,” Issa interjected. “If you have the right to fund the government, you have the right to fund the government to a lesser amount.”
Not funding is not the same as lowering funding.
The former ends a program the latter will force cost cuts or savings or reduced services to citizens. With Obamacare a law that made publicly subsidized healthcare among other things part of the US government, the Republicans want to not fund it. Not just fund it to a lesser amount.
Of course Republicans have the right to fund the government at a lesser amount…but they still have to fund the government.