By Manu Raju, Ted Barrett and Haley Byrd, CNN

(CNN) -- Republican senators said Wednesday that President Donald Trump should delay implementing the Mexico tariffs until he has made the case directly to them.

Members want him to appear before them next week so they can appeal directly to him about the tariffs and urge him to back down from his threat, which is set to take effect on Monday.

Republicans have openly expressed opposition to the tariffs -- but it remains unclear whether enough Republicans would break with Trump to override the tariffs altogether.

Instead, Senate Majority Leader Mitch McConnell has sought a delay in hopes of making the whole issue go away.

In a meeting Wednesday, he broached the idea of Trump meeting directly with members if talks between Mexico and the US fall through, according to senators.

Sen. Roy Blunt, a Missouri Republican and member of leadership, said that Trump should make his case in person to them.

"I think we have had in the past effective meetings with the President," he said, adding that 10-12 senators should meet with the president to express their concerns.

At issue is whether the President will declare a new national emergency to proceed with the escalating tariffs, which he announced last week on Twitter as a move intended to pressure Mexico into stemming Central American migrant traffic across the southern US border.

GOP Sen. Susan Collins of Maine agreed with Blunt's comments, adding "I think that the next step will be that a group of senators, probably led by the Texas senators who have obviously indicated their deep concerns, will go the President and talk to him about it."

On Tuesday night, one of those Texas senators -- John Cornyn -- referenced meeting with the President he hoped senators "as soon as he gets back" from Europe.

"We need to sit down with the President and talk about the way forward because I think this had a number of challenged, not the least of which is the USMCA," Cornyn told CNN.

Collins said the delegation could include other senators from the "states most affected."

"I am concerned that the administration always seems to resort to tariffs whenever there is a problem, whether it is immigration or trade or virtually anything and since the president's top priority is approval of the new trade treaty with Mexico and Canada I'm surprised he would seek to impose tariffs on Mexico at the very time he needs the Mexican governments support for ratification of the new treaty," said Collins, who is up in 2020

Other senators also up for reelection in 2020 raised concerns with Trump's approach.

Colorado Sen. Cory Gardner, one of the most vulnerable Republicans in the chamber, told CNN that he pushed back at administration officials at Tuesday's lunch, saying: "I don't think the Senate can support a tax and I hope they don't do it."

"I just don't see this majority's legacy being a tax-increasing legacy."

But Sen. Thom Tillis of North Carolina, who got sharply criticized for flip-flopping over the emergency declaration for the wall, is siding with Trump and has defended his approach.

Tuesday meeting meant to send a message

Senate Republicans on Tuesday said they've already sent an unmistakable message to the White House regarding Trump's threatened tariffs in an effort to stem the flow of migration into the US: You don't want us to vote on these tariffs, because you would lose.

That message, according to a Republican Senate aide, was delivered after two White House officials attended the GOP Senate lunch to explain the administration's legal reasoning behind the move.

Republican senators are signaling they would have more support for a resolution of disapproval to end the national emergency associated with any new tariffs than they had in March, when a dozen Republicans voted against Trump's use of emergency powers to seize funds for his border wall.

But whether or not they truly expect to shoot down Trump's decision -- or even have a veto-proof majority to do so -- is unclear.

It didn't help that the informational meeting provided little information for senators -- some said afterward that it seemed the White House still didn't know which path it would take.

"The way they put it was they're still working through all the details on it and they have not decided what their approach is going to be with regard to that," Sen. Mike Rounds, R-South Dakota, told reporters.

Veto-proof?

This isn't a vote many Republican senators want to have to take, and most members are still hoping the White House can change course after administration officials and Vice President Mike Pence meet with the Mexican delegation in Washington later Wednesday.

GOP leaders aren't saying whether they think they could have a veto-proof majority on the question. But, per McConnell: "There is not much support in my conference for tariffs, that's for sure."

If senators do revolt, there is still the House to consider. The last resolution of disapproval failed to override Trump's veto in the House, so members in that chamber would have to have a change of heart as well.

And some Republicans argue a disapproval resolution would undercut Trump's negotiating hand.

"I think the best thing to do is support his effort, because if we would be more united behind him, there would be a lot more people at the table negotiating a solution rather than just waiting for the next election," said North Dakota Sen. Kevin Cramer.

Members in Trump-friendly states who are up for re-election, like Sen. Thom Tillis of North Carolina, have danced around the issue, arguing border security is critical and that they would remain deferential to Trump on the issue.

The bottom line

There are still legal questions to be answered, depending on how the administration drafts the executive order or proclamation about the new tariffs. Republicans say they want to sort out the legalities first and want to talk directly to the President before they go into effect.

It is clear Congress won't be passing any legislation this week ahead of the Monday deadline for the tariffs to go into effect.

Congress has failed to take action against Trump's other controversial trade moves in the past, with Republicans preferring to lobby against his protectionism privately. But this time, Trump may have gone too far by threatening across-the-board tariffs on one of the United States' closest trading partners in the middle of the ratification process for his renegotiated NAFTA.

Republicans probably don't know if they have a veto-proof majority in the Senate just yet. And it's hard to overstate the fact that the 67 votes required to override a veto in the chamber is a difficult lift.

This story has been updated with additional developments Wednesday.