From what I have heard they haven't figured out what to do yet. The rep won't disappear as there would be huge uproar. Nobody has ever gotten a rep and lost it. Since if they remove the Utah rep then D.C. will probably lose it's or another state will lose their rep.
So here is the clever part: Utah was already forcasted next in line to get another rep based on population projections. So what would happen is that when the next reapportionment was done, Utah would simply keep the rep(unless some catastrophe wiped out half of Utah or something), and some state in the rustbelt would lose a rep. It's not really even unfair either, since the reapportionment simply mathematically reallocates the representatives according to population change(although the fact that states cannot have less than 1 rep makes small states "overrepresented" from a mathematical perspective).
I know I'm a bit of a "constitution worshiper" but, people throw "rights" around too freely. "I have a right to drive a vehicle!" "I have a right to own a house (regardless if they can afford or maintain it). "I have a right to free health care at the expense of others" instead of "I have a right to receive medical care". This is why I choose to just "stay" with the original ten. People don't understand what is really means to have "rights". To me, a right is something you are willing to die to protect. I'll gladly trade my life to ensure everybody rights to assemble, speech, etc.
Yes, plenty of people want stupid things, unfortunately, and I think other governments have shown that having a very difficult amendment process is a good thing. I simply think that this is a case of representation in government, which is something important enough to at least consider changing the constitution over. Some strict constitutionalists have used the constitution in an argument that almost implies that giving DC a rep under any circumstances would somehow be immoral and go against the founders' wishes. I personally think that is a load of crap.