Sorry for not answering sooner, PHXMama - just saw your post.
I'm not sure that I'm the "best" to answer, but I'll give you my opinion on the US side at least. Before the US/HP rumors started in 2005, I would have bet good money that I wouldn't have a job to retire from in Nov 2006. US was literally doing whatever it could to keep the doors open regardless of the long-term impact.
By the time BK exit/merger rolled around in Sept 2005 US was running out of cash - $410 million on hand heading into the winter months when it had burned through $417 million in the Dec 2004 - Feb 2005 period.
For the longer view, US ended Nov 2004 (the second month of BK) with $823 million in cash - more than when it entered BK. An increase in cash tends to occur when you can stop paying pre-BK bills but still collect the money from ticket sales. By the end of Feb 2005, cash had dropped to $406 million - that drop of $417 million I mentioned above. Then cash started increasing again, reaching $559 million by the end of May 2005. That's Air Whiskey's $125 million in DIP financing, refunds of airplane deposits/progress payments from Airbus, Embraer, and Bombardier in exchange for canceling all outstanding aircraft deliveries, plus the Easter/Spring Break/start of summer travel periods (there were operating profits in Mar/Apr/May). Then cash started dropping again, reaching $410 million by the end of Aug 2005 (the last full month before BK exit/merger). Without the cash infusion that came with the merger, I doubt US would have lasted to Spring 2006 - all sources of new cash without selling off more assets had been exhausted. Maybe, just maybe, selling assets (slots, gates, TA routes, airplanes, etc) could have extended that, but it would just have been putting off the inevitable at that point. The creditors could have pulled the plug at any time as they watched the assets their payoff depended on disappearing.
HP's future sans merger is basically an unknown for me. Looking at the quarterly reports during the pre-merger year or so, HP seemed to be sorta holding it's own. At the end of 2Q05, the last quarter prior to the merger, HP has a little more cash than US had at the merger but was quite a bit smaller with disproportionately smaller expenses. So on a cash as a percentage of expenses basis, HP was in quite a bit better position than US. Likewise, HP's spread between CASM and passenger RASM was significantly better than US' - about 1.2 cents deficit vs 2.0 cents. In other words, HP needed less cargo/other revenue per ASM to break even than US did.
How HP would have done given the large increase in jet fuel prices, especially in 2007 and so far in 2008, is something I can't even speculate about - especially with the large amount of WN competition in PHX/LAS with their fuel hedging advantage added to their cost advantage. If I had to give my gut feeling on the fate of each as stand-alone carriers, HP would have been in trouble in the 2007/2008 time frame (trouble meaning BK), but US would have been gone by mid to late 2006.
I'll now return everyone to their original thread.....
Jim