Public health officials working to make a potential COVID-19 vaccine available to all Americans said they need more than $25 billion to make it happen, but the continued impasse between the Trump administration and congressional Democrats on another coronavirus relief package has stalled that much-needed funding.

Centers for Disease Control and Prevention Director Robert Redfield and Bob Kadlec, assistant secretary for preparedness and response at the Department of Health and Human Services, raised the alarm Wednesday, saying that the agencies have depleted $600 million in previously appropriated COVID relief aid and added they still don't have enough funding to fulfill the goals of getting a free COVID-19 vaccine to everyone in the country.

Redfield said at this point the CDC does not have the resources to distribute a vaccine across the country, including infrastructure to accommodate transporting and storing doses at cold temperatures.

"We need substantial resources and the time is now to get those resources out to the states, and we currently don't have those resources," he told members of a Senate Appropriations Subcommittee on Wednesday.

But President Donald Trump painted a different picture at a White House news conference Wednesday evening.

Asked by a reporter about Redfield saying earlier, under oath as he testified before the Senate, that a vaccine will be "generally available to the American public" in the "late second quarter, third quarter 2021," Trump deemed it "incorrect information."

"I don't think he means that," Trump said. "I don't think he -- when he said it, I believe he was confused."

"I saw the statement," he added. "I called him and I said what did you mean by that? And I think he just made a mistake. He just made a mistake. I think he misunderstood the question probably."

The White House hopes to begin distributing doses of a coronavirus vaccine within 24 hours of emergency approval, and states have been told to be prepared by November. But Redfield told lawmakers earlier Wednesday not to expect widespread distribution so soon.

"If you're asking me when is it going to be generally available to the American public, so we can begin to take advantage of vaccine to get back to our regular life, I think we're probably looking at third, late second quarter, third quarter 2021," Redfield told senators.

Trump also contradicted Redfield at his briefing when he said the CDC director "made a mistake" and misunderstood the question when he said that masks are more effective than a vaccine.

"Face masks are the single most important public health tool we have," Redfield said during his testimony to the Senate while holding up his surgical mask.

"Number 1 it's not more effective than a vaccine," Trump said during his briefing from the White House hours later. "I called him about it. Those were the two things I discussed with him. If you asked him, he would probably say that he didn't understand the question because I said to him. I asked him two questions. The one we covered and the mask question."

The president added, "It's not more effective. I think there's a lot of problems with masks. Vaccines are much more effective."

A spokesperson for Redfield initially gave ABC News a statement that the director in his testimony had intended to convey that most Americans would complete their vaccinations around summer 2021. An hour later, however, Redfield’s office rescinded that statement.

It was not immediately clear if Redfield was standing by his original testimony -- at odds with the president -- or would be issuing a new statement.

Meanwhile, Democratic leaders have insisted on a sweeping fifth stimulus package -- at least $2.2 trillion -- but Senate Republicans and the White House have demanded that the number be far lower. Trump threw a curve ball to his party leaders on Wednesday though, tweeting, "Go for the much higher numbers, Republicans, it all comes back to the USA anyway (one way or another!)."

Redfield said in his testimony it will take somewhere between $5.5 billion and $6 billion "to get all 64 jurisdictions ready to implement" his agency's distribution plan.

And Kadlec, who works with the efforts to manufacture vaccines ahead of potential authorization by the Food and Drug Administration, said they need an additional $20 billion to have 300 million doses of a vaccine available.

"We have basically worked to basically do simultaneously the clinical trials, as well as doing the manufacturing of vaccines. So, if and when -- whether that's two weeks, three weeks, two months or four months -- once a clinical trial is complete and that scientific data is reviewed by the FDA and approved, then we have vaccine potentially available immediately to us," Kadlec said of Operation Warp Speed, the Trump administration's plan to expedite vaccine allocation.

"We need to figure out a way to do this. ... Now is the time," Subcommittee Chairman Roy Blunt, R-Mo., told ABC News Wednesday. Blunt suggested that perhaps Congress could agree to some piecemeal approach, but so far, Democratic leaders have refused.

Lawmakers on the subcommittee that oversees HHS funding also raised concerns that money they appropriated for COVID-19 response was being used for other things, including concerns from Democrats about reports that the agency is soliciting a $250 million contract for a communications firm to convey a hopeful message to the American public about the end of the pandemic.

"We have two deputy secretaries of HHS before us today and neither one of them can testify as to whether that contract was awarded, why it was awarded, what the reasons for it were," Sen. Chris Murphy, D-Conn., said during the hearing.

"It's increasingly impossible for any of us to know who's in charge," he added. "We've got two people at the highest echelon of HHS that can't answer questions about a massive contract that's been awarded."

Redfield said the CDC was not involved in that contract or working to develop its message, just that the agency was told to transfer money to HHS.

"CDC received the direction from HHS and OMB (the Office of Management and Budget) to transfer $300 million to HHS," Redfield told Murray.

"We haven't been involved in this, other than the extent that the funds were transferred to HHS and so I assume that they're going to come back to the different subject matter experts, but again we haven't been involved in that," he said. "You know if given the opportunity that CDC would obviously want to put forth the accurate messaging for the American public."