Popular sentiment is the public punished the Republicans severely for shutting down the Government during the Clinton administration. But the losses in the following 1996 elections amounted to two seats in the House of Representatives. Republicans gained two seats in the Senate. Clinton bowed under pressure to institute welfare reform and budget cuts, and Republicans maintained control of Congress. The result of the governmental shutdown was not the stinging rebuke from the electorate the media or Republican leadership would have us believe.
The media went apeshit and was mean to sitting Congressmen, but in the end, the shutdown had little effect on the Party and a significant effect on policy going forward. Clinton won the propaganda war, the Republicans won the policy war. I will take that every time.