Sen. Mark Kirk on Tuesday became the first Republican senator to meet with Merrick Garland, President Obama’s Supreme Court nominee.

The senator from Illinois, who is facing a competitive re-election this fall, slammed his GOP colleagues, some of whom have flatly refused to meet with Garland or even consider holding confirmation hearings.

“I think we should do our jobs,” Kirk told reporters after the meeting, adding that he hoped other Republicans will follow his lead.  “We need a rational, adult, open-minded consideration of the process.”

Kirk is perhaps the most endangered Senate Republican facing re-election in November. And when it comes to the battle over Obama's pick to fill the court vacancy, Kirk has been an outlier.

He's one of just three Senate Republicans to say the Senate Judiciary Committee should hold hearings on Garland. And he's one of two GOP senators -- along with Susan Collins, R-Maine -- to say the full chamber should vote on the nominee.

"I think when you just say I'm not going to meet with him and all, that's too closed-minded," Kirk said Tuesday.

Republicans, led by Senate Majority Leader Mitch McConnell, R-Ky., insist that Obama's successor should fill the Supreme Court vacancy after American voters have a say in November. The death last month of conservative Justice Antonin Scalia created the court opening, and Obama is pressing to make his third appointment to the high court.

"By leading by example, I'm showing what a rational, responsible guy would do that really wants the constitutional process to go forward," Kirk said.

The senator called Garland "one of the most eminent jurists in the country."

Democrats have been insisting that the Senate go through the regular confirmation process for Garland, the chief judge of the U.S. Court of Appeals for the District of Columbia Circuit. With most public opinion polls showing majorities favoring action on Garland, the Democrats' goal is to force GOP senators to buckle under pressure or make some of them facing re-election pay the price on Election Day.

At least 13 Senate Republicans have said they'd be willing to meet with the federal judge, though many said they would tell him that he won't get a vote.

Earlier this month, Kirk said on a Chicago radio program that the Senate should "man up and cast a vote."

Garland has met with seven Democratic senators.

The Associated Press contributed to this report.