Chuck Schumer said Judge Neil Gorsuch favoured the "powerful over the weak" and failed to answer "question after question" in his confirmation hearing.
Senate Democrats are in a 48-52 minority but can insist that Mr Gorsuch wins 60 votes, a so-called filibuster.
Republicans could then revert to a simple majority in a "nuclear option".
That would require them voting in a change of rules.
Mr Schumer's announcement is sure to set up a bruising battle.
He said he did not think Judge Gorsuch would be a mainstream judge.
"After careful deliberation, I have concluded that I cannot support Judge Neil Gorsuch's nomination to the Supreme Court," Mr Schumer said.
"He will have to earn 60 votes for confirmation. My vote will be 'no', and I urge my colleagues to do the same," he added.
If Mr Gorsuch did not get 60 votes, "the answer isn't to change the rules, it's to change the nominee," Mr Schumer said.
Judge Gorsuch is on the fourth and final day of his confirmation hearing before the Senate Judicial Committee, where outside parties comment for or against his nomination.
Thursday's first witness, the American Bar Association, gave Judge Gorsuch its highest rating of "well qualified".
The committee will vote, probably next week, on the nomination. It simply records a favourable, unfavourable or "without recommendation" comment and passes the final decision to the full Senate.
Senate Republicans say they will seek a full vote on the chamber floor before Congress leaves for recess on 7 April.
It is unclear how many, if any, Senate Democrats would support Mr Gorsuch's nomination. He would need eight to beat the filibuster.
The so-called nuclear option would require Republicans to change Senate rules to allow Mr Gorsuch's nomination to be approved with a simple majority.
President Trump has called on them to do so if necessary.
During the confirmation hearing, Democrats on the committee regularly expressed their anger that President Barack Obama's nomination for a post that was vacated 13 months ago was refused a hearing by Republicans.
Republicans blocked Merrick Garland's nomination, arguing it should not go ahead in an election year.
Mr Gorsuch, 49, would restore a 5-4 conservative majority on the Supreme Court that lapsed with the death of Justice Antonin Scalia.
As a lifetime appointee, Judge Gorsuch would join the other justices in having the final legal word on many of the most sensitive US issues.
Judge Gorsuch's qualifications have not been called into question at his hearing, but Democrats have been frustrated at his refusal to signal any stance on such emotive areas as gun control, abortion and employee rights.
He has simply said it is his duty to apply the law as it stands.

The Scot, who retired from racing last year, is joining forces with UK motorsport authority the MSA for the scheme.
The former Williams test driver said: "I knew I wanted to give something back when I stopped racing."
The scheme will start with motorsport, but there are plans to expand it into other male-dominated environments.
Wolf said: "I never set out to become a role model but somehow I did.
"The opportunities are out there. We aim to inspire female talent to ensure in the long term our sport is diverse."
It will be officially launched at the Autosport International Show at Birmingham's NEC on Thursday 14 January.
Wolff spent three years involved in test and development work at Williams, and took part in four practice sessions at grands prix over the 2014 and 2015 seasons.
Before that, she spent seven years driving for Mercedes in the German touring car championship (DTM).

The woman, who has not been identified, was working in the city with a non-governmental organisation.
Police said she was asleep when a security guard at the hotel where she was staying entered her room and attacked her.
The woman is receiving treatment for cuts and bruises, and legal assistance.
Doctors told reporters that the woman was in stable condition and had been visited in hospital by the district magistrate.
According to police, she had been visiting Varanasi for more than 40 years and would stay there for long periods of time.
Scrutiny of sexual violence in India has grown since the 2012 gang rape and murder of a student on a Delhi bus.
However, brutal sexual attacks against women and children continue to be reported across the country.
The leading Democrat in the US Senate says he will lead an attempt to block President Donald Trump's nomination for the Supreme Court.
[NEXT_CONCEPT]
Susie Wolff is launching an initiative aimed at increasing the number of women involved in motorsport.
[NEXT_CONCEPT]
Indian police have arrested a man in connection with the rape of a 70-year-old French woman in the northern city of Varanasi.