The link offers nothing to support your claim that Harry Reid said that "any Blagojevich appointment couldn't possibly represent the people of Illinois"

This Huffington Post link comes closer, but still does not validate what you have claimed.

It is truly regrettable that despite requests from all 50 Democratic Senators and public officials throughout Illinois, Gov. Blagojevich would take the imprudent step of appointing someone to the United States Senate who would serve under a shadow and be plagued by questions of impropriety. We say this without prejudice toward Roland Burris's ability, and we respect his years of public service. But this is not about Mr. Burris; it is about the integrity of a governor accused of attempting to sell this United States Senate seat. Under these circumstances, anyone appointed by Gov. Blagojevich cannot be an effective representative of the people of Illinois and, as we have said, will not be seated by the Democratic Caucus.

Next week we will start one of the most important debates of the year - outlining an economic recovery plan to create jobs and invest in America. And in the coming weeks, we will be working to protect homeowners and consumers, make America more energy independent, strengthen our national security, and improve health care and educational opportunities. There is much work to do and a lot at stake. It is thus critical that Illinois and every other state have two seated Senators without delay.

We again urge Gov. Blagojevich to not make this appointment. It is unfair to Mr. Burris, it is unfair to the people of Illinois and it will ultimately not stand. The governor must put the interests of the people of Illinois and all Americans first by stepping aside now and letting his successor appoint someone who we will seat."

Senator Harry Reid

Do you really believe that Burris, as a Blogojevich appointed Senator could represent Illinois effectively? He will end up looking tainted as hell:

Burris, his lobbying firm, his clients and a law firm that includes him donated $127,986 to Blagojevich since the governor took office. Burris himself gave $4,500 to the governor, including $1,000 last June. His lobbying firm, Burris & Lebed Consulting, gave $10,796 in cash and services. The law firm with which Burris is affiliated kicked in $5,000 for the governor. Burris' consulting firm has gotten $294,546.30 in state contracts under Blagojevich.

Burris' lobbying clients -- which were under contract with the state for $3.09 million while he represented them -- contributed $107,690 for the governor.

Dave McKinney and Chris Fusco, "Blagojevich names Roland Burris to Obama's Senate seat", Chicago Sun-Times, December 30, 2008

I am not intimating any wrongful actions here. Any person appointed by a governor who will soon be facing a Federal Indictment, who has already been arrested in a criminal complaint, alleging a play-for-pay scheme as a part of the appointment process is going to get tainted, and Burris, along with entities he is affiliated with, have ponied up substantial campaign contributions for Blogojevich. This will only get uglier as it progresses, and the GOP will feast upon it.

Reid is right. He has not said that any Blogojevich appointment cannot represent Illinois, he said that any Blogojevich appointment cannot "effectively" represent Illinois. There is a big difference between these two statements. Be careful what you wish for; it may come true...