With regards to Clinton's numbers in New York in 2000, you have to remember that she was at a disadvantage not being a native of the state. Lazio essentially had the home state advantage like Bush in Texas in the Presidential race.
Her 2006 numbers will be more indicative of her overall vote getting ability. Whether or not she pulls a higher percentage of the vote than Kerry or Gore got in New York will be meaningful.
It would be meaningful against a credible opponent, but it appears that Hillary won't have a credible opponent.
The best shot was Jeanine Pirro, and she made a fool of herself. The state's Republican party has imploded, and can't even field a candidate for governor, much less senator.
Under these circumstances, I'm not sure how meaningful Hillary's percentage will be as an indicator of how she can perform nationally.
In 2000, she ran below Gore in New York by about 4 points, and that could be telling. Since Gore essentially tied the race nationally, that can only mean that Hillary would definitely have lost.
I wish she had a credible opponent in 2006 because I agree with your theory and would love to see it tested, but I think the circumstances of this particular race undermine the operation of your theory.
True, obviously the quality of the opposition is a key factor. However, it will still be interesting to see how many Republicans vote for Clinton, as opposed to just staying home or voting third party or voting for the third-tier Republican nominee.
If she is intensely hated, I would think that she would not do well against any opponent in conservative areas of the state.
