Speaking with conservatively minded friends on this subject, they just shrug it off, smug in the knowledge that if they were in that situation they would immediately be able to pull themselves out of it. The fact that other people don't just do that is because they make poor decisions and therefore its all about 'personal responsibility'. There really is no convincing them otherwise.
I was talking to a conservative chap the other day during the SNAP crisis and he was foaming at the mouth that SNAP needed to be abolished. I asked him what to do about the people with disabilities who couldn't work. He told me he knew personally of two people born without arms or legs who have factory jobs earning $45/hour and have no need of SNAP and therefore anyone disabled who was claiming SNAP was a scammer. And if they really are that disabled, he went on, then their family should be taking care of them and not the state.
p.s. this person has also never paid taxes in his entire life because "government is a scam"