Trump's pick Judge Neil Gorsuch had failed to get 60 votes required to get a simple majority confirmation vote in the 100-seat Senate. Forty-four Democratic Senators said they oppose the nomination of Gorsuch.
The Democratic blocking tactic, known as a filibuster, has never until now been successfully employed to block a Supreme Court nominee in the American history.
The opposition Democratic party is making every effort to block the nomination as that the Republicans had successfully blocked the Supreme Court pick of former US President Barack Obama last year.
This means that the Republican party would require 51 votes to get the confirmation of Gorsuch.
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"It would be a radical move, something completely unprecedented in the history of our Senate, and out of all proportion to the eminently qualified judge who is actually before us," he said.
"It really is up to them and to how we should proceed. But one way or the other, we will confirm Judge Gorsuch," said Senator John Cornyn, another top Senate Republican.
However, Senate Minority Leader Charles Schumer warned that the Senate was about to go over the cliff.
"The 60-vote bar in the Senate is the guardrail of our democracy. When our body politic is veering too far to the right or to the left, the answer is not to dismantle the guard rails and go over the cliff, but to turn the wheel back toward the middle," Schumer said.
The only nominee on the Court to be confirmed with less than 60 votes was Justice Thomas, who is widely recognised to be the most ideological extreme Supreme Court justice, he said.
Senator Johnny Isakson, said that Gorsuch is an exceptional nominee with the right judicial temperament and a strong reliance on the text of Constitution and laws.
"I am extremely disappointed by the blind obstruction carried out by Senate Democrats today. The Senate and our country are headed in a dangerous direction if this type of partisan behaviour continues," he said.