"This administration has simply not looked at problems which [missile defence] creates; they've only looked at the fact that there is a threat," he said.
Thursday's defection of Senator Jim Jeffords from the Republican party gave the Democrats control of the Senate and the power to block much of Mr Bush's agenda.
Democrats are anxious about the estimated $60bn cost of the missile shield, the impact its development would have on relations with Russia and China and doubts about whether the technology will even work.
Carl Levin, the incoming chairman of the Senate Armed Services Committee, said he was concerned about unilateral action and the possible impact of violating the 1972 Anti-Ballistic Missile treaty.
"This administration has simply not looked at problems which [missile defence] creates; they've only looked at the fact that there is a threat," he said.
"There are much greater threats to which we are not addressing resources," Mr Levin added.
Mr Jeffords' defection changes the balance of power in the Senate to 50 Democrats, 49 Republicans and one independent.
Republicans control the House of Representatives, 221-210, with two independents and two vacant seats.
Nato concerns
The defence shield has caused concern even among the closest of US allies in Nato, who view the ABM treaty as a linchpin of global security.
That appeared to be uppermost in Mr Daschle's mind.
"If you're asking should we violate the ABM Treaty; if you're asking should we alienate every ally, and Russia and China besides; if you're asking should we commit to something, deploy something that still hasn't been shown to work, I'd say no," he said.
However, Washington's allies have kept quiet about their concerns after Mr Bush's pledge to consult them about a plan that is still a long way off.
Bush undeterred
On the Republican side, Bush aide Andrew Card on CBS's Face the Nation said realignment would not deter the administration from pressing ahead with its plans.
Outgoing Senate majority leader Trent Lott, meanwhile, said Mr Jeffords' decision was a mistake and he dismissed suggestions that Mr Bush had sidelined moderate Republicans.
"The White House is doing everything they need to do. They bear no blame on this," Mr Lott said on ABC's This Week.
He also suggested that there might be a shift back to a Republican majority in the next 18 months.