Steele called the outcome in Massachusetts a "repudiation" of Democrats' health care overhaul legislation pending in Congress, saying 41 Republican votes in the Senate now effectively kills the bill in its current form. Democrats needed to retain 60 votes to prevent a Republican filibuster.
"Start from scratch. Start by listening to the people," Steele advised his Democratic colleagues on health care.
Brown had campaigned in opposition to the Obama health care proposal, saying he would vote against the bill if elected.
"One thing is very, very clear as I travelled throughout the state," Brown, a lawyer and former model, said in his acceptance speech last night. "People do not want the trillion-dollar heath care plan that is being forged."
But many Democrats rebutted the notion that Brown's victory is a major statement on Obama and the Democrat's legislative agenda, including health care overhaul.
"We won the House and Senate in 2006, we won the White House in 2008. ... People sent the unmistakable message they wanted change. We have to deliver on that," former Obama campaign manager David Plouffe said on 'GMA.'
"The Republicans have chosen their path: they are doing the bidding of insurance companies, just as they're going to do with big banks as it relates to financial reform. We have a good health care plan and we need to pass that," Plouffe said.
The White House has previously deflected suggestions that a Brown victory would amount to a referendum on the Obama presidency, vowing to move ahead on its agenda.
"I think there's a tremendous amount of upset and anger in this country about where we are economically," White House press secretary Robert Gibbs told reporters Tuesday.
Asked whether he believed Americans are now attaching that frustration with Washington to Obama, Gibbs said, "I think there is certainly some attachment to us."
Watch George Stephanopoulos' exclusive interview with President Obama tonight on "World News" and "Nightline." Check your local listings.
Still, the administration and many Democrats plan to continue pursuing their agenda "full speed ahead."
Senate Majority Leader Harry Reid said Tuesday night the loss of the 60-vote majority will not change the Democrats' priorities.
"While senator-elect Brown's victory changes the political math in the Senate, we remain committed to strengthening our economy, creating good-paying jobs and ensuring all Americans can access affordable health care," Reid said in a statement. "We hope that Scott Brown will join us in these efforts. There is much work to do to address the problems Democrats inherited last year, and we plan to move full speed ahead."
Although Democrats no longer have the votes needed to thwart a Republican filibuster, they maintain the largest Senate majority either party has enjoyed since 1979 and still have the ability to pass legislation through reconciliation, a process that bypasses normal Senate rules by requiring only 51 votes.
Brown has said he opposes Democrats' health care overhaul working its way through Congress, leaving Democrats scrambling to develop contingency plans for the bill's passage.