Majority Leader Mitch McConnell left the Senate to address House Republicans’ weekly conference meeting Tuesday morning. His message was simple: Senate Republicans will hold fast to their promise not to advance a Supreme Court nominee.

Rep. Tim Huelskamp, R-Kan., summed up the closed-door appearance this way: “Mitch McConnell said to members, ‘Read my lips: No new Supreme Court hearings until we have a new president.'”

The message came before McConnell and Senate Judiciary Chairman Chuck Grassley, R-Iowa, walked into a likely negotiations storm at the White House later Tuesday. President Obama along with top Democrat lieutenants was expected to work over the duo in the Oval Office.

At issue is which president will nominate someone to replace the late Justice Antonin Scalia.

Democrats say Obama has a right to name Scalia’s successor, and the Senate has a duty to consider the nominee. But Republicans reply that that’s a job best saved for after the election and the inauguration of a new president.

“The Senate should not consider any nominee until after the election,” McConnell wrote in a commentary, “when the people have spoken, and we have a new president.”

Since Scalia’s Feb. 13 death, GOP leadership has remained consistent in that message.

No one appeared to leave the meeting with Obama and Vice President Joe Biden with a different opinion than they brought to the Oval Office.

If Republicans were “willing to meet with the president,” Senate Minority Leader Harry Reid, D-Nev., told reporters, “they could at least meet with the president’s nominee.”

And in a written statement, Grassley said consideration of a nominee during an election year would do significant harm.

“Whether everybody in the meeting today wanted to admit it,” Grassley wrote, “we all know that considering a nomination in the middle of a heated presidential campaign is bad for the nominee, bad for the court, bad for the process, and ultimately bad for the nation.”

McConnell and Grassley weren’t expected to budge. White House spokesman Josh Earnest admitted that a specific conversation about nominees would be “a pretty dramatic reversal in position for Mr. McConnell.”

Senate Democrats are more bullish. They have said Republicans eventually will crack under mounting public pressure. Sen. Chuck Schumer, D-N.Y., predicted that Republicans will relent, as they have during similar hotly contested battles.

Sen. James Lankford, R-Okla., dismisses that forecast.

The freshman senator, who also addressed the House conference Tuesday, said he doesn’t “see any signs of the GOP blinking on this one, to say the least.”

Lankford said, “That’s wishful thinking from Democrats and Schumer, who in 2007 said President Bush shouldn’t have any more nominees in his final year, with 18 months left in his term.”

It wasn’t McConnell’s first visit to the House side of Congress. The majority leader last week huddled with members of the conservative House Freedom Caucus as part of an ongoing campaign to build Republican resolve.

Carrie Severino, chief counsel for the conservative Judicial Crisis Network, praised that effort—and McConnell—for keeping Republicans “admirably unified” on the Supreme Court vacancy.

Though the House won’t play an official role in the fight over the next Supreme Court nominee, congressmen will do much to shape public opinion.

McConnell is “attempting to explain and educate,” Severino told The Daily Signal.

Whether that lesson sticks, Senate Republicans will have to stay unified to keep Scalia’s seat on the Supreme Court open until after Obama leaves office Jan. 20.

Public opinion could swing against them. A national survey of more than 1,000 Americans by Pew Research Center found that 56 percent say “the Senate should hold hearings and vote on Obama’s nominee.”

This report has been updated to reflect the White House meeting.