Mr. Chang,

The New York Times indeed failed to offer a speculation as to why Whites are convinced that Obama as President would not "be" a future reality improving race relations. Thus my own answers can at best be only provisional and speculative (by the way, I am a White male).
Many Whites may believe that an Obama Presidency would not improve race relations because of a fear alluded to in books such as "Whitewashing Race" and the very pessimistic little text called "Hopes or Fears: Black Candidates, White Voters." This is the idea that Obama as President would be accountable to Black community interests, which they view as being in opposition to their own (this one perception isn't necessarily false, as any redistributive measures implemented to close racial inequality gaps must entail some degree of collective White loss). They perceive that Obama would either enact or facilitate a whole range of policies which they do not happen to like; and battles over these policies would inevitably fall substantially along racial lines and entail a great deal of racial friction.
A somewhat less likely (but still present) possibility is how White MINORITIES (my emphasis) have reacted to their dethronement from directly controlling selected foreign nations. The official end of apartheid in South Africa in 1994 has had obvious benefits but has not closed racial polarization gaps in that country. Black South Africans remain largely loyal to the African National Congress. Not only have White South Africans failed to come over to the ANC, but they continue to vote for Right Wing parties in South Africa's multiparty system.
An odd example of this phenomenon of enduring resentment was when I made an entry in my poorly read blog about the death of a former apartheid-era President, Piet Botha. A White guy in South Africa wrote me back stating he thought that my biographical summary of Botha ("The Crocodile") was pretty good. Responding to him and looking up his own link on Blogspot.com, I noticed that his site contained a number of superb photos of the natural beauty of South Africa. I asked him if he worked in the nation's tourism industry and he replied, "No. I guess I'm not Black enough for Thabo Mbeki and the ANC." This was an expression of a guy who resented any affirmative action initiatives being taken in the new South Africa; and any redistributive losses imposed upon White people this might entail.
White minorities have largely just fled from former European colonies now controlled by native majorities. When Robert Mugabe became President of Zimbabwe, the heavy majority of Whites simply left the country--and this was long before his high profile farm takeovers/seizures. Likewise in Algeria the French settlers, called the "Pieds Noirs," all ran away from the country immediately upon its' independence and coming under Arab majority rule in July 1962.
Many White Americans will not like the initiation of a racial "changeover" in America which may slowly get underway under an Obama Presidency. This would be the same reality as White Southerners being generally unhappy when Jim Crow fell. Social change in the 1960s meant that a full-blown White Supremacy regional society was changing into something of a multiracial society--a "new day" which they did not care for at all. The unhappiness of White Southerners some 40+ years ago might be writ large to the entire nation during an Obama Presidency and its' continuing aftermath.
So while it's absurd to pretend that racial minorities in the U.S. have been and are happy under White Conservative hegemony and control, it may prove equally absurd to believe that Whites will be happy under a social order of greater minority empowerment, which among other things may entail an overall more Left national politics which they also won't like. Racial POWER relations in the United States could very well change eventually, but EMBITTERED race relations never will. Thus that portion of Dr. King's Dream where the races live together within a context of harmony rather than polarization will never happen. Whites will become the "champion whiners" in the America of tomorrow ironically in the same way that they viciously stereotype minorities today.