The White House Covid czar says he’s still optimistic about more aid, despite recent Republican objections.

President Biden’s coronavirus response coordinator said Thursday that he remained optimistic that Congress would approve billions of dollars in new emergency aid to fight Covid, even as Republicans on Capitol Hill have made clear the aid package is all but dead.

“I’m an eternal optimist,” the coordinator, Dr. Ashish K. Jha, told reporters during a White House briefing. “I remain convinced that Congress is not going to walk away at this point in the pandemic, when we have made so much progress.”

But while Dr. Jha may be an optimist, the mood among Senate Republicans is pessimistic; some even assert the White House lied to them earlier this spring when officials said that, without new aid, the administration would have no money to purchase vaccines and antiviral drugs. More recently, the White House said it was taking money out of other programs to buy the drugs and shots.

On Capitol Hill, lawmakers are consumed by a bipartisan package of gun safety legislation and eager to get out of town for the imminent Fourth of July recess. Approving Covid-19 aid is not on the immediate agenda.

Dr. Jha’s remarks came as the Biden administration is focused on rolling out coronavirus shots for newly eligible children as young as 6 months old. He said that the White House had so far delivered more than four million doses of pediatric vaccine for children in that age group, but that the administration would not know how many doses had been administered until next week. The Pfizer-BioNTech protocol for the very young requires three shots, while Moderna’s requires two.

One concern is whether the vaccines, which have often been administered in pharmacies, will be as readily accessible to the very youngest children as they were to other age groups. A federal law, the Public Readiness and Emergency Preparedness (PREP) Act, was amended to authorize pharmacists to administer Covid vaccines only to those age 3 or older.

At the same time, many parents may be reluctant to have their young children vaccinated at pharmacies, said Dr. Rochelle Walensky, director of the Centers for Disease Control and Prevention. They “want to take their younger kids to where they routinely get vaccinated, whether it’s their local community health center or their local pediatrician,” she added.

For those reasons, administration officials say they have gone to great lengths to enlist pediatricians in the childhood vaccination program.

Dr. Jha, Dr. Walensky and Dr. Anthony S. Fauci, Mr. Biden’s top medical adviser for the pandemic, used Thursday’s briefing to promote childhood vaccination.

“The known and potential benefits clearly outweigh the known and potential risks in this pediatric population,” said Dr. Fauci, who is recovering from his own bout with the coronavirus, adding, “We are all very enthusiastic about getting your children vaccinated.”

Dr. Walensky addressed parents directly: “The most important thing to do is to get your child vaccinated, get your family vaccinated, and that will deliver the most protection to you and your family and allow you to not be at risk of severe disease.”

And Dr. Fauci, 81, attributed his resilience more than a week after testing positive — “I’m feeling really fine” — to being vaccinated and double-boosted, saying he viewed himself as “an example, given my age, of what we’re all talking about today.”

“And I believe if that were not the case,” he said referring to having received a full complement of shots and boosters, “I very likely would not be talking to you looking as well as I look, I think, right now.”