Speaker Mike Johnson is kicking off the new year by leading more than 60 House Republicans to the U.S.-Mexico border on Wednesday, in a bid to raise pressure on President Biden and Democrats to agree to strict new immigration policies to choke off the flow of migrants streaming into the country.

During a visit to Eagle Pass, Texas, Mr. Johnson is expected to attack Mr. Biden for the surge in migrant crossings and demand that he crack down by deporting people who try to enter the country illegally and resuming construction of a border wall. The visit comes as Senate Republicans and Democrats are struggling to reach an agreement on border policy changes that the G.O.P. has demanded as the price of supporting emergency spending legislation that would speed more than $50 billion in military assistance to Ukraine.

The talks have centered around making it more difficult for migrants to claim asylum in the United States, deporting or detaining more of those who cross the border and keeping more of them out of the country while they await a decision on whether they will be allowed to enter. Mr. Biden and Democrats in Congress, recognizing the political liability they face if they fail to address the border, have signaled openness to some changes, but not enough to satisfy Republicans. And in the House, Republicans are pressing for even more severe measures that Democrats are unlikely to embrace.

“This situation requires significant policy changes and House Republicans will continue advocating for real solutions that actually secure our border,” Mr. Johnson said Tuesday in a post on social media.

Republicans in both the House and Senate have insisted that sweeping immigration changes must be part of any bill to help Ukraine fight off a Russian invasion, and G.O.P. senators last month blocked a $110.5 billion national security spending bill that would replenish Kyiv’s war chest. Their demands prompted Biden administration officials, including Alejandro N. Mayorkas, the homeland security secretary, to join near-daily bipartisan talks on Capitol Hill last month to find an elusive compromise on immigration policies — a reflection of the political pressure Democrats face to impose order on the border.

Senators resumed those negotiations in person on Tuesday afternoon after holding them virtually over the last week with participants scattered around the country for the holidays.

Biden administration officials declined on Tuesday to discuss the details of the talks but said, speaking on condition of anonymity because the negotiations are private, that they were moving in the right direction.

Late last month, Senator James Lankford, Republican of Oklahoma and the G.O.P.’s lead representative in the talks, said negotiators had made “significant progress.” Senator Mitch McConnell, Republican of Kentucky and the minority leader, said in a joint statement with Senator Chuck Schumer, Democrat of New York and the majority leader, that they were equally “committed to addressing needs at the southern border and to helping allies and partners confront serious threats in Israel, Ukraine and the Indo-Pacific.”

But members of Congress have failed for decades to come together on immigration policy, one of the thorniest and most politically fraught issues they have faced. And Mr. Johnson has repeatedly signaled that House Republicans will only accept an agreement that reflects their own hard-line bill, meaning that any bipartisan deal struck in the Senate could still collapse in the other chamber.

“Democrats across the country are starting to recognize reality: there must be transformational change to secure the border and end the crisis caused by President Biden’s destructive polices,” Mr. Johnson wrote in a post on X last month. He sent a letter to Mr. Biden condemning Mr. Schumer for disbanding the Senate for the year without putting a House-approved bill reinstituting Trump-era border policies to a vote in his chamber.

On Tuesday, one of the Biden administration officials said that Mr. Johnson and House Republicans were playing politics rather than working to enact meaningful changes.

Part of Mr. Johnson’s strategy reflects the pressure he is getting from the right. G.O.P.’s hard-liners openly oppose the Biden administration’s efforts to arm Ukraine. And Republicans have made a draconian approach to border security — including an overhaul of the nation’s asylum laws and a return to detention policies that forced migrants to wait in Mexico before making their case to a judge — a centerpiece of their 2024 campaign message.

On Tuesday, Representative Chip Roy, Republican of Texas and one of the far right’s loudest voices, dismissed Mr. Johnson’s border visit as a weak gesture. Instead, he said, Republicans should refuse to fund the federal government until the administration either cracks down on cross-border migration or Mr. Biden signs the House-passed border enforcement bill into law.

“It’s time to act with urgency,” Mr. Roy wrote in a letter to his colleagues, adding that he would “refuse to fund — or otherwise empower — the United States government, or any foreign government it is supporting, unless and until it fulfills its constitutional obligation to defend our borders from invasion.”

The threat is a potentially potent one, coming as Congress faces back-to-back deadlines to fund the federal government on Jan. 19 and Feb. 2. Senate leaders have been eyeing the two deadlines as possible opportunities to have lawmakers vote on a Ukraine-border deal, should negotiators succeed in producing one — despite the fact that Republicans and Democrats have yet to agree on the size of the next spending bill.

But significant gaps remain between the two parties that would make it difficult for negotiators to finalize an agreement before Congress returns to Washington next week. Though the two sides have agreed in principle to make it more difficult for migrants to apply for asylum, increase detentions and broaden the president’s ability to swiftly deport those who cross the border illegally, they remain at odds over how and when such powers should be used — and how to write those authorities into law.

Hamed Aleaziz contributed reporting.