The Republican border blitz enters a new phase next week with a field hearing at Pharr, Texas, this time trying to make the case that the homeland security secretary, Alejandro Mayorkas, has intentionally created chaos at the border, which led to last week’s kidnapping.

The visit by members of the House Committee on Homeland Security next Wednesday will come in response to the kidnapping of four Americans at Matamoros, Mexico, last Friday. Two of these Americans, who’d reportedly entered Mexico in search of discounted “tummy tuck” procedures, were found dead Tuesday; another was injured and the fourth was relatively unharmed.

The chairman of the homeland security committee, Representative Mark Green, has blamed the attack on the “weak posture that the Biden administration has taken with its perilous border security policies.”

“Clearly, these dangerous cartels have mastered how to use Biden and Mayorkas’s failed border policies to their advantage in both Mexico and the U.S. homeland — and Americans are suffering because of it,” Mr. Green said.

The new volley of criticism of Mr. Mayorkas comes as President Biden tacks toward more conservative Trump-era border policies and after it appeared the House was backing down from attempts to impeach Mr. Mayorkas.

On Tuesday, the White House press secretary, Karine Jean-Pierre, refused to comment on whether the administration was considering reinstating a policy of detaining migrant families, suggesting that a return to the policy is a possibility.

This change in policy would come as a response to Republican rhetoric on the issue, as well as to 2022 seeing a record-breaking 2.76 million border crossings.

Early in the year, Republicans in the House were pushing toward the impeachment of Mr. Mayorkas and alleging that he intentionally maintained an “open border.”

“No question the secretary of homeland security deserves impeachment, not because he’s failing on the border but because it’s on purpose,” Representative Matt Gaetz told Real America’s Voice in late February.

According to Mr. Gaetz, though, “enough Republicans will oppose the impeachment of Mayorkas to stop it in its tracks.”

Other members of the House have suggested that they would like to go further than impeachment, with Representative Clay Higgins alleging that Mr. Mayorkas has committed negligent homicide, assisted criminals, and is responsible for “thousands of murders.”

“If I could arrest you for violations of Louisiana revised statutes I would,” Mr. Higgins said at a congressional hearing.

Mr. Mayorkas has defended himself, insisting that he has been performing his duties lawfully during an unprecedented time of migration in the Western hemisphere.

House Republicans like Representative Jim Jordan have insisted that America does not maintain operational control of the border, which he has argued should be grounds for impeachment.

Mr. Mayorkas has rebutted these claims, telling CNN that the department’s goal is “to achieve operational control of the border, to do everything that we can to support our personnel” during a time of unprecedented migration.

The secretary has also called on Congress to overhaul the immigration system, a task that some members of Congress had hoped to address in the final days of the 117th Congress.

Any action on immigration and border security in the House, however, appears to have stalled out in committee, despite the repeated visits to the border.

Although some 33 bills concerning immigration and border security having been introduced to the 118th House, there are no votes, committee markups, or hearings scheduled on the issue, save the one next week.

The most prominent of these bills, the Border Safety and Security Act of 2023, introduced by Representative Chip Roy, has been awaiting consideration by the homeland security and judiciary committees — chaired by Messrs. Green and Jordan, respectively — since January 9.

While any measure passed in the House would likely face long odds in the Senate, there are senators who have insisted there is the potential for a bipartisan deal.

In a January trip to the border, one of those, Senator Cornyn, the Republican of Texas, was joined by Senators Kelly and Coons, both Democrats, and Senators Tillis, Lankford, and Moran, indicating some amount of bipartisan support for legislation in the Senate.

The framework for such a deal would be to combine increased border security measures with a pathway to citizenship for “Dreamers” who have been allowed into the country, giving members of both parties incentives to vote for the bill.

In the meantime, the number of border crossings, which saw a modest decline in January, is expected to ramp back up with the end of Title 42, a pandemic-era measure allowing for the expulsion of migrants, which is expected to end with the lifting of the Covid state of emergency in May.