(NewsNation) — Homeland Security Secretary Alejandro Mayorkas on Wednesday acknowledged before Congress a crush of migrant crossings at the southern border will come after the expiration of Title 42, a controversial Trump-era border policy.

“A significant increase in migrant encounters will strain our system even further, and we will address this challenge successfully,” Mayorkas said. “But it will take time.”

Mayorkas testified Wednesday before a subcommittee on the House Appropriations Committee and is expected to get a grilling from Republicans when he testifies before the House Judiciary Committee for the first time Thursday.

A 60-page memo from Rep. Jim Jordan (R-Ohio), a ranking member on the committee, that was obtained by The New York Times suggests Republicans plan to accuse Mayorkas of encouraging illegal immigration with “far-left policies.” 

Republicans have made it clear they intend to make immigration and border security pillars of their midterm campaign and hope to get Mayorkas to personally address the issue.

Some of the points in the memo link migrants to sex offenses and warn that they could be criminals by pointing to arrests at the border. 

House Republicans stated in a letter sent before Mayorkas’ testimony, “your failure to secure the border and enforce the laws passed by Congress raises grave questions about your suitability for office.”

The Biden administration has faced bipartisan pushback on its plan to lift the pandemic-era Title 42 border policy.

Mayorkas on Tuesday released a memo outlining a more robust effort to enforce U.S. immigration law without the use of Title 42.

“When the Title 42 public health order is lifted, we anticipate migration levels will increase, as smugglers will seek to take advantage of and profit from vulnerable migrants,” Mayorkas said in the memo.

In response to Republican lawmakers demanding specifics about how the government will handle a surge, Mayorkas said, “We started our planning last September, and we are leading the execution of a whole-of-government strategy … to prepare for and manage the rise in noncitizen encounters.”

The Department of Homeland Security announced a six-point plan that the White House says will increase staffing and resources at the border, decrease overcrowding, ramp up expedited removal efforts and bolster the capacity of nonprofits to handle migrants while they’re being processed.

The remaining two pieces of the plan will target smugglers and drug traffickers and discourage irregular migration.

The May 23 expiration of Title 42, which lets border officials turn away migrants on public health grounds, is being challenged.

Senate Minority Leader Mitch McConnell, (R-Ky.), said Tuesday that Republicans “are going to insist” on a vote on keeping Title 42 in place, likely as an amendment to a compromise $10 billion package of pandemic aid.

The Supreme Court heard arguments Tuesday over the continuation of another contentious immigration policy known as “Remain in Mexico.” 

The policy forces those seeking asylum to remain on the Mexican side of the border while waiting for their cases to be adjudicated. 

Mayorkas, in an October order to end “Remain in Mexico,” reluctantly conceded that the policy caused a drop in weak asylum claims but said it did not justify the harms.

“This is the Biden border crisis. There are no ifs, ands, butts about it,” said Sen. John Thune, (R-S.D.). “There has never been a more direct correlation between a set of policy decisions and consequences from those decisions that what we’ve seen at the border.”

The Hill and the Associated Press contributed to this report.