Representative Max Miller, the increasingly embattled Republican from Ohio who was accused of physically abusing his ex-wife and young daughter, continued to resist pressure on Friday to drop his re-election bid as the deadline for him to withdraw neared.

Mr. Miller planned to loan his campaign $1 million, according to a person familiar with his thinking who spoke on the condition of anonymity to describe campaign strategy, effectively rebuffing calls from powerful Republicans in the state to withdraw from the race.

Senator Jon Husted, who faces his own tough re-election battle, broke his silence Thursday by publicly urging Mr. Miller to “step aside as a candidate and resign from Congress.” And on Friday, the head of an Ohio-based conservative group, the Center for Christian Virtue, posted on social media that Mr. Miller had “disqualified himself.”

Ohio state law gives local party leaders until 4 p.m. on Monday to name a new candidate, but the law requires two days of notice to convene a meeting to do so. Mr. Miller would most likely have to end his congressional campaign either by Friday or Saturday, though officials have said there is still some confusion about the deadline.

The effort by G.O.P. leaders to push Mr. Miller off the ballot has been underway for at least a week, ever since his contentious custody battle with his ex-wife, who is the daughter of Senator Bernie Moreno, burst into the national news. The public push has intensified as the deadline has neared.

Mr. Miller also tried to defend himself by embarking on a media tour that included a lengthy and erratic interview with CNN’s Jake Tapper, in which he struggled to answer straightforward questions such as when he had last used illegal drugs, alarming Republicans even more.

Officials said they feared that the seriousness of the accusations could cost the party a comfortably Republican seat that it cannot afford to lose in a midterm election cycle in which control of the House is at stake.

Mr. Miller’s ex-wife, Emily Moreno, whom he met while they both worked on the 2016 presidential campaign of Marco Rubio, has accused him of holding a gun to her head, throwing scalding hot water at her and fracturing the collarbone of their young daughter. At the Capitol this week, Mr. Moreno also told reporters that Mr. Miller had refused to turn over his daughter’s favorite stuffed animal, a blue bunny, during custody exchanges.

Mr. Miller has vehemently denied the allegations and accused his ex-wife and former father-in-law of fabricating stories to sabotage his career. He told President Trump in a phone call earlier this week that he planned to do as the president had done amid his own scandals: fight through it. Mr. Trump urged him to consider his odds, but he stopped short of requesting his withdrawal.

Some Republicans in the state, including Vivek Ramaswamy, who is in a tight contest for governor, have stayed quiet. House Speaker Mike Johnson told Politico that an Ethics Committee investigation, which Mr. Miller requested, should “play out.” Others have come to Mr. Miller’s defense.

“To represent a district like this, you have to work. And Max Miller is a hard worker,” said Jim Trakas, the former chairman of the Cuyahoga County Republican Party. He stressed that the accusations against Mr. Miller were in the context of “two people who got divorced and disagree with each other about how to raise a child.”

Mr. Miller had been scheduled to lead a rally on Monday in Strongsville, a suburb of Cleveland, with Representative Anna Paulina Luna, a Republican of Florida. He will no longer be there.

Shannon Burns, the chairman of the Strongsville G.O.P., said the cancellation was due to threats to his safety.