The future of the homeland security secretary’s impeachment trial is uncertain, with a majority emerging in the Senate who could seek to kill the effort before it begins and the House delaying sending the articles to the upper chamber to buy time.

Secretary Mayorkas was impeached on the second attempt by the Republican-controlled House in February for alleged mishandling of the situation at the southern border and for lying. Both he and the White House have dismissed the impeachment as campaign messaging for Republicans.

On Tuesday, House leadership signaled that it would delay sending articles of impeachment to the Senate for a trial after Republican senators signaled that there might not be support in the upper chamber to even hold a trial. Republicans insist the Senate has an obligation under the Constitution to hold the trial.

“To ensure the Senate has adequate time to perform its constitutional duty, the House will transmit the articles of impeachment to the Senate next week,” a spokesman for Speaker Johnson, Taylor Haulsee, told CNN. “There is no reason whatsoever for the Senate to abdicate its responsibility to hold an impeachment trial.”

The articles of impeachment were supposed to be delivered to the Senate on Wednesday. However, Senator Schumer has signaled that he plans to offer a motion to dismiss the impeachment, which would only need a bare 51-vote majority to pass.

“We’re going to try and resolve this issue as quickly as possible. Impeachment should never be used to settle policy disagreements,” Mr. Schumer said. “It’s absurd and there are no charges in the House complaint that rise to the level of impeachment.”

As it stands, there are 51 Democrats in the Senate and 49 Republicans. Even in the event of a Democratic defection, Vice President Harris could break the tie.

One of the most frequent defectors from the Democratic conference, Senator Manchin, has signaled he is ready to dismiss the impeachment. A Democrat turned Independent who caucuses with the Democrats, Senator Sinema, has remained silent on the issue, noting that she doesn’t preview her votes.

Beyond the Democratic majority in the Senate — which Republicans knew they would have to confront to get an impeachment trial — not every Republican seems to think an impeachment trial is merited.

On Thursday, a group of 43 Republican senators signed a letter demanding that Senate Democrats hold a trial for Mr. Mayorkas. Six Republicans in the Senate, Senators Romney, Collins, Paul, Cassidy, Murkowski, and Tuberville, declined to sign the letter.

Since then, at least one senator, Mr. Cassidy, appears to have come out in favor of an impeachment trial, saying in a video Friday morning that “Democrats love impeachment trials until they don’t love impeachment trials.”

“Right now — best I can tell — Majority Leader Chuck Schumer, Democrats, are not going to hold a trial, they’re embarrassed by it. We need to hold a trial. Hold the trial, Chuck,” Mr. Cassidy said.

Mr. Tuberville, though he did not sign the letter, had also previously come out in favor of holding an impeachment trial and has also signaled that he would vote to convict.

Ms. Murkowski and Mr. Romney have said that they think an impeachment of Mr. Mayorkas would be a waste of the Senate’s time. Ms. Collins and Mr. Paul have been mum on the issue.

“I am more than a little bit frustrated that we’re going to be taking up an impeachment process that most everybody understands is really nothing more than a messaging effort,” Ms. Murkowski told Alaska Public Media on the issue.

Ms. Murkowski explained that she agrees that the administration has mishandled the border but is concerned that the impeachment would force the Senate to put down all other business, like budget and national security bills.

She also said that she doesn’t see any of the charges leveled by the House rising to the level of “high crimes and misdemeanors,” a sentiment echoed by Mr. Romney.

Some senators have begun a public pressure campaign against their colleagues in the hopes of stirring up support. However, even if they are able to get a Senate trial, there is little chance of the Senate convicting Mr. Mayorkas since two-thirds of the chamber would need to support his ouster.

“DHS Secretary Alejandro Mayorkas has been impeached by the House of Representatives,” Senator Cruz said in a tweet. “The Senate has a constitutional obligation to hold the trial.”