The House is set to vote on Tuesday on impeaching Alejandro N. Mayorkas, the homeland security secretary, on charges that he has willfully refused to enforce border laws and breached the public trust, as Republicans pursue a partisan indictment of President Biden’s immigration policies.

Republicans are pressing forward despite the assessment of legal experts, including some prominent conservatives, that Mr. Mayorkas has not committed high crimes and misdemeanors, the constitutional threshold for impeachment. If they succeed, which would take near unanimity among the G.O.P. given the party’s tiny majority, Mr. Mayorkas would become the only sitting cabinet member to be impeached in American history.

The move is an escalation of Republicans’ efforts to attack Mr. Biden and Democrats over immigration, as the two parties clash over how best to secure the border during an election year when the issue is expected to take center stage in the presidential campaign.

House Republican are pushing forward with the impeachment as they work to kill a bipartisan deal that emerged in the Senate pairing a fresh infusion of funding for Ukraine with a border crackdown. They have argued that the measure is too weak and that neither Mr. Biden nor Mr. Mayorkas can be trusted to secure the border.

With Democrats solidly opposed to the impeachment effort and expected Republican absences, Republicans can afford to lose no more than two of their own members on the vote. One Republican, Representative Ken Buck of Colorado, has already stated his opposition, and a handful of others have yet to declare their positions.

Leaders of the impeachment effort, however, have expressed confidence that Mr. Mayorkas will be indicted.