"I'm for whatever works," McConnell told reporters on Tuesday. He also suggested he'd be open to new legislation that would make it more difficult for shutdowns to happen in the first place.
Congressional Republicans, feeling the political pain of the 35-day partial government shutdown that ended last week, are eager to go into the new talks not only unified, but with a conciliatory image.
"A shutdown is a bad idea and remains a bad idea. And I'm optimistic we will not be in that position yet again," McConnell said.
Republicans have faced trouble both internally and among constituents since the dispute over Trump's wall triggered the shutdown.
McConnell's approval rating was 15 percent in the Jan. 25-27 Monmouth University national poll, the same as the survey's previous finding in November. But House Speaker Nancy Pelosi's approval number doubled to 34 percent in the latest poll.
McConnell, who traditionally has an iron grip on Senate Republicans, saw his hold start to fray last week. Sen. Ron Johnson, a Republican from Wisconsin, told McConnell at last week's party caucus the shutdown is "your fault." And six Republicans voted Thursday for a Democratic plan that would have reopened the government.
This week all is well again.
"He's working in the right direction," Sen. Mike Rounds, a South Dakota Republican, said of McConnell. Rounds said senators were frustrated because the Senate had failed to take up any legislation as McConnell had been largely invisible as the shutdown dragged on. McConnell has insisted it would be wasting time to vote on legislation that Trump didn't support.
McConnell's decision last week to put up two competing pieces of legislation, however, showed the White House that Senate Republicans don't have the votes for Trump's wall.
"It's a good thing Mitch McConnell emerged from the witness protection program to help lead the Senate forward," suggested House Democratic Caucus Chairman Rep. Hakeem Jeffries, a New York Democrat.
The negotiators meeting Wednesday are charged with finding common ground not just on a border barrier, but on a wide range of strategies to bolster security. Unless agreement is reached by Feb. 15 on funding nine Cabinet agencies, including homeland security, as well as several smaller agencies, the government would shutter again.
The 17-member committee, appointed by congressional leaders, includes 10 House members and seven senators. Nine members are Democrats. Eight are Republicans. They are members of their chambers' appropriations committee, which write spending bills, and most are regarded as pragmatic deal makers. If the negotiators agree on legislation, it would have to be approved by both Houses.
Pelosi has been adamant: No wall. And Democrats Tuesday were reluctant to say just what they would accept. Some have suggested they'd be open to backing about $1.6 billion for more fencing along the Rio Grande. The Republican-dominated Senate Appropriations Committee last year approved a homeland security funding bill that included the money.
"I thought it was a good place to start, some of the Democrats thought it was too much later on, and the president didn't think it was enough," noted Sen. Richard Shelby, an Alabama Republican who chairs the committee.
Sen. John Hoeven, R-North Dakota, said he hoped the compromise would follow U.S. Customs and Border Protection recommendations.
"Let's rely on them and I think they'll lay out what they need, where they need it and what it looks like," he said.
Many Senate Republicans are worried that Trump would set a dangerous precedent by declaring a national emergency.
"Congress needs to get its job done," said Sen. Cory Gardner, R-Colorado.
In the House, Republicans tried to show that differences over barriers need not be legislatively fatal.
Trump told reporters on Jan. 4 that he could officially declare a national emergency to build a border wall but wants to try to negotiate a border wall with Congress.
He said he had spoken to Trump about the language.