A bipartisan group of negotiators in the Senate who are trying to craft an immigration reform and border security bill are saying they will push forward to finalize the agreement despite disparaging comments made by Senator McConnell and President Trump. On Wednesday, conservatives went after Mr. McConnell for the secret talks, only to have Mr. McConnell reportedly tell colleagues in private that he has little confidence that the deal will get done. 

Punchbowl News is reporting that Mr. McConnell told GOP senators at a Wednesday meeting that his party faces an uphill battle in finishing the deal as Mr. Trump is running hard on closing the southern border.  On this issue, Mr. Trump is more trusted by voters than the incumbent president, according to recent polling. 

“Politics on this have changed,” Mr. McConnell told colleagues. Of the 45th president, the Senate minority leader said: “We don’t want to do anything to undermine him.”

According to exit polls conducted by CNN at both the Iowa caucuses and the New Hampshire primary, the most important issue for Republican voters is immigration. In the general election, President Biden is uniquely weak on the issue. A recent Monmouth University poll shows 28 percent of voters approve of how he handles the border and immigration, while 68 percent disapprove. 

Mr. Trump has been pressing Republicans to ditch the negotiations. “I do not think we should do a Border Deal, at all, unless we get EVERYTHING needed to shut down the INVASION of Millions & Millions of people, many from parts unknown, into our once great, but soon to be great again, Country!” he wrote on Truth Social. 

The Democrats’ negotiator, Senator Murphy, was visibly fatigued when speaking with reporters on Thursday but said he would continue to push for the deal despite Mr. Trump’s comments.

“I hope we don’t live in a world today in which one person inside the Republican Party holds so much power that they could stop a bipartisan bill to try to give the president additional power at the border to make more sense of our immigration policy,” Mr. Murphy said. “I’m just going to keep my head down. I’m working with partners who want to deal.”

Some Republicans do want the negotiators to keep going because the crisis needs to be addressed now rather than after the next election. “I think the border is a very important issue for Donald Trump,” Senator Romney told reporters on Thursday. “And the fact that he would communicate to Republican senators and congresspeople that he doesn’t want us to solve the border problem because he wants to blame Biden for it is really appalling.”

Senator Young called the former president’s foray into the negotiations “tragic.”

Negotiators “have been working very hard to secure the southern border to give the next president, whomever it is, more authority so that we can secure the southern border,” Mr. Young said. “Anything that interrupts that negotiation would be tragic. I hope no one is trying to take this away for campaign purposes.”

Senator Tillis, who has been party to some of the negotiating sessions, says his fellow Republicans are letting the perfect be the enemy of the good. He had previously gotten into a shouting match with Senator Cruz when tension erupted over the deal during a Republican luncheon earlier in the week. 

“Biden has failed,” an animated Mr. Tillis told reporters on Thursday. “We are here. We have been elected. We have election certificates. When you have the opportunity to make this country safer, you take it and you don’t play politics.”

The Republican lead negotiator, Senator Lankford, who has been famously tight-lipped about the deal, told Fox News on Thursday that his colleagues are tired of being left in the dark about the exact provisions of the bill, saying the legislation should be put in their hands as soon as possible. He did warn, though, that it isn’t going to look like the House-passed immigration and border deal known as H.R. 2. 

On Wednesday, before Mr. McConnell told his colleagues that he may pull out of the negotiations, a group of Senate conservatives went at their conference leader for coordinating with Senator Schumer on the agreement while keeping everyone else guessing. 

“It’s the law firm of Schumer McConnell” that is trying to expedite the deal, Senator Lee said. “That is uncollegial to a degree I lack the capacity in the English language to describe.”