The emerging bipartisan border deal is hitting fresh snags among Republicans on Capitol Hill because of the opposition of former President Donald J. Trump, who is closing in on his party’s presidential nomination at a critical time for the agreement.

Senator Mitch McConnell of Kentucky, the minority leader, told Republicans privately on Wednesday that the politics of the issue had been complicated by Mr. Trump’s rise and his hostility to the agreement, putting the party “in a quandary,” according to lawmakers who participated in the meeting and described his comments on the condition of anonymity.

The remarks, reported earlier by Punchbowl News, were striking coming from a Republican who has toiled to distance himself and his party from the former president. Mr. McConnell has vociferously backed the proposed border compromise and has been a chief proponent of a stalled effort to send tens of billions of dollars in military aid to Ukraine, which Republicans have said must be tied to the deal.

Mr. McConnell’s abrupt change in tone reflected the increasingly difficult challenge facing Senate negotiators as they race to finalize immigration legislation that the former president is already actively campaigning against.