You have made the wrong assumption, and thus you are asking the wrong questions.
You assume that conservatives thought that inflation was going to be rampant (because, well, they said those words). Instead, the real thought was "we can't do anything that boosts the economy when Obama is in office since that would make Obama look good". That is why we couldn't pass a jobs bill, couldn't pass an infrastructure bill, needed to audit the fed, couldn't have low interest rates since we temporarily worry about inflation, etc. Once you realize that they aren't worried about inflation, but are instead worried about Obama looking good, then you see why they can't admit to being wrong about inflation. They were never actually worried about inflation to begin with.
This is a good and interesting point! We know that conservatives don't care about budget deficits as they happily run them up when in control of government. Deficit worries are simply a useful tool with which to attack social welfare spending they don't like. Considering that deficits affect inflation rates it does stand to reason that they don't care much about inflation either, simply finding it a useful tool to inhibit economic growth when unfriendly politicians are in power.
A few things could argue against that though. One is that inflation decreases the real value of debts, and debts are overwhelmingly held by rich people. Also somewhat related (and conveniently argued with) is that low interest rates reduce the spread banks can make on loans, reducing their profitability. As banks and rich people seem to be two constituencies that the GOP genuinely does care about I could see how they care about inflation. Not for the reasons they claim, but because it helps rich people.