The President staked out a tough position after Republicans warned he would not get a vote on his eventual nominee to replace the late Justice Antonin Scalia. The GOP is arguing that filling the seat on the nation's highest bench should be left to the next president.
"The Constitution is pretty clear about what is supposed to happen now," Obama said during his first press conference since Scalia's passing over the weekend.
Obama took a swipe at Republicans by saying he was amused to hear some in the party describe themselves as "strict interpreters" of the Constitution but dispute the idea that he has the right to get a hearing for a Supreme Court nominee.
"I am amused when I hear people who claim to be strict interpreters of the Constitution suddenly reading into it a whole series of provisions that are not there," he said. "I am going to present somebody who indisputably is qualified for the seat and any fair minded person, even somebody who disagreed with my politics would say would serve with honor and integrity on the court."
He added: "Your job doesn't stop until you are voted out or until your term expires."
Obama also weighed in on the 2016 presidential race, hinting heavily that he did not believe that Donald Trump was qualified to be president and is convinced the billionaire Republican front-runner would never reach the White House.
"I continue to believe Mr. Trump will not be president," Obama said, adding that he viewed the American people as too sensible to put someone like the former reality star in the White House.
The Supreme Court nomination battle is putting control of the White House, Congress and the Supreme Court on the line this November. Democrats hope that voters will consider the GOP's refusal to undertake that process as a sign of obstruction and overreach that could cause a backlash against Republicans and help Democrats take back the Senate.
On the one hand, and despite the GOP gambit, the President could decide to find the candidate he believes has the most stellar legal qualifications and thus increase political pressure on Republican Senate Majority Leader Mitch McConnell for a vote.
But given that his pick is unlikely to even have confirmation hearings, Obama could chose to nominate a "sacrificial lamb" who would delight the Democratic Party's liberal base voters and motivate a high turnout in November's election.
Some court watchers have suggested a compromise candidate, possibly a moderate Republican, whom it would be difficult for GOP Senate leaders to snub -- for example someone like Utah Sen. Orrin Hatch.
Hatch told CNN on Tuesday that he didn't think he would be nominated.
"That's kind of a joke. I'll be 82 in March. They're not going to put an 82-year-old man on there," he told CNN's Chris Cuomo on "New Day."
"Of course if they decided to do that, I'd have every Democrat praying for my demise. If they did do that, and it's not going to happen, but if they did, I would spend the next 20 years making sure that I did the job."
In his news conference, the President bemoaned what he styled as the wider sweep of Republican obstructionism in the Senate which he said threatened the proper functioning of nation's political institutions.
"This is the Supreme Court and it's going to get some attention. We have to ask ourselves as a society, a fundamental question, are we able to still make this democracy work the way it's supposed to, the way our founders envisioned it?" Obama asked.
He challenged anyone who adheres to a strict reading of the Constitution to come up with a reason why his nominee did not at least deserve a hearing.
"It's pretty hard to find that in the Constitution," Obama said.