In the U.S. House: representatives serve for two years (all house representatives are up for re-election every two years)
In the U.S. Senate: senators serve for 6 years (only one-third of the senators are up for re-election at a time - 1/3 in 2012, 1/3 in 2014, 1/3 in 2016 and so on)
Even though the elections will be held in November 2012, the current Congresspersons hold their seats until any new folks are sworn in the first week of January 2013.
So, to answer your question The House and The Senate do NOT dissolve before or even after election day. The first week of January 2013 the next session of Congress will begin and that will be the 'date' of the first day that any newly elected office holders will begin their term of office.
I hope I typed that out clearly and that it makes sense