Vice President Mike Pence said Wednesday that Neil Gorsuch, President Trump's nominee to fill a vacancy on the Supreme Court, would invite every senator to sit down with him ahead of what could be a contentious confirmation process.

"If they take the meeting, he's going to meet with all 100 members of the Senate," Pence said during an interview on the "Rush Limbaugh Show" radio program.

"I think the president and our entire team are heartened by some of the early responses" to Gorsuch, Pence added.

Trump unveiled his decision to nominate Gorsuch, a conservative appellate judge from Colorado, during a prime-time announcement on Tuesday evening in the East Room of the White House.

Although some Democrats, such as Sen. Elizabeth Warren, quickly expressed opposition to Gorsuch, a handful of others urged their colleagues to allow an up-or-down vote on his nomination.

Pence said he has been surprised by the deluge of critical media coverage the Trump administration received during its first two weeks.

"I will tell you the negative media coverage ... has been striking to me," Pence said. "I have to tell you that in all of my life, there's always been a grace period" for new presidents, he said.

"And boy, if there was a honeymoon, it was pretty short," Pence joked.