The top Republican on the Senate’s environment panel and leading EPA critic predicted Friday that the president’s yet-to-be-named nominee to replace Lisa P. Jackson as EPA administrator will be confirmed.

Despite speculation that confirmation for a successor to Jackson may be difficult, Oklahoma Republican James M. Inhofe said enough Republicans will likely defer to President Barack Obama’s nominee to reach the 60-vote threshold necessary to defeat a filibuster.

“Unless there’s something really negative, you’ll find a lot of Republicans go over to that side — recognizing that it should be the prerogative of the president,” said Inhofe, the ranking member on the Environment and Public Works Committee. “And I don’t agree with that because I think that’s why they have confirmation.”

Jackson, whose four-year tenure at the EPA unfolded in an unusually bitter political environment, announced Thursday that she will leave the agency after next month’s State of the Union address to pursue unspecified new opportunities.

At the EPA, she oversaw a suite of sweeping regulations to control greenhouse gases and other power plant emissions, as well as a crackdown on pollution from mountaintop removal mining. In doing so, she was the public face of what critics called the Obama administration’s “war on coal.”

While Inhofe has been one of the most strident critics of EPA policies, he has had only the kindest words for Jackson, with whom he spoke this week.

He said Friday the two sparked a surprise friendship when she first called him after Obama nominated her in 2009. “We hit it off at first,” he said, noting that Jackson keeps a picture of his family in her office. “She’s been a very decent person.”

In the next Congress, Louisiana Republican David Vitter will replace the term-limited Inhofe as ranking member on the environment panel. Vitter promised in a statement “to make sure the new EPA nominee is thoroughly vetted, puts sound scientific standards above political ideology, and understands that a continuing avalanche of overregulation can crush economic recovery.”

He also has claimed that Jackson’s resignation was sparked by reports that she used the email pseudonym “Richard Windsor” to conduct official business, allegations the agency’s inspector general is investigating at the request of House Republicans. Vitter said the matter highlights what he calls the administration’s “culture of hiding an extreme agenda from Americans because it can’t be sustained in public debate.”

The EPA has said Jackson used the secondary email account for communications with other officials, since her public email address is widely known and the account is flooded with messages. The agency said the practice was followed for many years by Jackson’s predecessors. The EPA has said it welcomes the inspector general’s review.

The White House declined to comment on the timing of a nominee to replace Jackson, but signaled that EPA Deputy Administrator Robert Perciasepe will take over as acting administrator if a successor has not been named and confirmed by the Senate. While a 1998 law (PL 105-277) imposes time limits on temporary appointments to positions requiring Senate confirmation, the statute also includes waivers of the constraints that can allow acting officials to serve almost indefinitely.

Lisa Murkowski of Alaska, the ranking Republican on the Appropriations subcommittee that funds the EPA, said Friday she has reservations about seeing the agency run by an acting official for an extended period.

“Both from the administration’s perspective and from those of us who are trying to figure out what’s going on within the department, and budgets and initiatives, it helps to know who you’re dealing with,” she said.

Murkowski declined to comment on whether she would support Perciasepe or current EPA air chief Gina McCarthy — another rumored internal candidate — if either was nominated by Obama, but said both may benefit from having been confirmed previously by the Senate.

“It might be easier for those who have gone through that process once and who lawmakers have some familiarity with,” she said.

Murkowski said she would have reservations about another rumored candidate, California Air Resources Board Chairwoman Mary D. Nichols, who is currently overseeing implementation of that’s state’s sweeping climate change law.

Nichols “is one that would face some real questioning from me,” she said.