Was this just an off the cuff remark
It was a central part of his
speech to the Indian Parliament.
or something the administration actually wants to do?
It was very useful though for a number of reasons - Obama pretty much put India on notice for how it will act during it's upcoming temporary rotation on the Council; it gave him cover for what was otherwise a somewhat confrontational speech in parts (see references to nuclear non-proliferation; Burma); and it isn't something Obama needs to worry about actually implementing any time soon, if at all.
Does the coalition that supported the Brazil-India-Germany-Japan permanent SC seats back in the nineties still exist?
Yes
I believe that deal/proposal also hilariously included a veto seat that rotated between big African nations.
Various proposals have existed regard boosted African representation - but I'm not aware of any (serious) proposal that proposed extending veto power to anyone - nevermind random African states.
Perhaps more importantly, does the coalition that opposed it still exist? IIRC, Mexico and Argentina opposed Brazil's bid, Pakistan opposed India, the Netherlands and a few other European countries opposed it in favor of a permanent EU seat or some such, China and South Korea opposed it for regional reasons, and a few countries like Canada opposed it on principle.
Yes, pretty much. Internal EU opposition to Germany has been waning though.
Canada doesn't oppose in principle (except officially, no doubt) - they're concerned about a dilution in their status. (That they lost the recent Council elections probably won't help either.)