"We again urge Governor Blagojevich to not make this appointment," a statement from senior Democratic leaders said on Tuesday.
"It is unfair to Mr Burris, it is unfair to the people of Illinois and it will ultimately not stand."
Blagojevich was arrested on December 6 and accused of plotting to sell off the US president-elect's vacated senate seat.
He has denied the corruption charges and branded efforts to impeach him for his alleged role in the senate seat scandal as politically motivated.
He has also repeatedly defied calls to resign from Obama and other party leaders.
Burris, 71, was the first African-American elected to state office in Illinois in 1978 and was the state's attorney general from 1991 to 1995.
In 1984, he lost the US senate Democratic primary and was again defeated a decade later in a run for governor. He also ran unsuccessfully for mayor in Chicago.
He is currently a lawyer in a private practise in Chicago.
The US constitution says the senate decides the qualifications of its would-be members, however if the senate blocked the appointment, the case could end up in court.
Last week an internal investigation by Obama's team cleared Obama and those on his transition team of any inappropriate contacts with the Illinois governor.
The case has proved an embarrassing distraction to the president-elect as he prepares to enter office on January 20.
The Democrats will control of the US Senate with at least 57 seats in the 100-seat chamber when congress reconvenes on January 6 next year.
However Obama's former senate seat and one in the state of Minnesota currently remain undecided.