Well to be fair, those who dislike the ACA do so on opposite ends of what to do. The split is almost 50/50 on kill it or fix it according to the latest Pew poll so CONs are playing silly numbers games trying to make it seem the majority want ACA killed. Pew also shows those who know more about the law have a much higher opinion of it and those who live in states that have set-up the health insurance exchanges have a much higher opinion than those where the states has left the exchange up to the Federal Government.
Now when it comes to not funding a law past by Congress the CONs are playing silly games, I doubt many Americans see what they are doing as 'good' and if the Senate refuses to consider the GOP based budget plan I don't think the public will blame Reid or Obama.
The House GOP poll has a large majority(71) of Americans NOT in favor of shutting down government as a way to force defunding of ACA, Even CONs are 53% against it. Poll by David Winston.
The Pew Research Center has GOP self identification down to 19% of those polled. pg 8 july 17-21. dem 29% indie 46%
Hart Research has a candidate committed to fixing the ACA winning by 15% over a candidate vowing to kill it.
According to a Faux Noise poll done sept 6 and 9- 22% of CON voters favor ACA while only 14% favor 'Obamacare' so it does appear there is some simple knee jerk reaction to the President's name.
So I tend to believe the ACA is here to stay, the only real issue is how to work on making it better. Call that what you wish but that is closer to the true will of the people...

eace