1.) The District of Columbia gets three electoral votes via the 23rd Amendment, but does not get a second bite at the apple when any Presidential election has to go to the House for resolution, as ONLY States voting as Delegations have a say at that point.
2.) The 'Quorum' problem you mention would not be one for two reasons. The first is that it would only take ONE Republican present to vote for his State if all the Democrats sat out the special session. In the current House of the 108th Congress there are 7 States which have NO Republican Representatives and there are 8 States with NO Democrats as Representatives. To prevent a quorum in this situation for the next House in the 109th Congress, there would have to be 26 State delegations with no Republicans, and if that condition were met, then the Democrats would control enough delegations to elect their own candidate. Secondly, there is NO other business before the House but electing a President. No other business may be taken up until there is a new President. I don't think that anyone would try to out wait the American public in that case.
3.) The current House of the 108th Congress would NOT be the one to witness the count the Electoral College votes for President, and if no majority was to be had then vote on a new President by State delegation. That duty would belong only to the newly elected House of the 109th Congress which is seated in January 6th of 2005.
4.) If a State delegation is 'tied', then it just votes 'present' during any Presidential voting in the House.
Below is a data table for the current House of the 108th Congress as of the date of this post. I would expect that Texas would move from a tie to solid Republican, for 31 Republican delegations. There may be some other shifts in the composition of some other State delegations, but I do not see the House of the 109th Congress having any fewer than the necessary 26 delegations necessary to re-elect President Bush if the House would have to make the choice.
US House - 108th Congress
by State
by Delegations
Source: Office of the Clerk, US House of Representatives OFFICIAL LIST OF MEMBERS OF THE HOUSE OF REPRESENTATIVES of the UNITED STATES
Hope this helps...
dvwjr
Thanks to you and others for the excellent fact based answers.