"If they want to give us more money, that's okay; we'll take more money," Trump said during a press briefing last week .

But Trump said he was not opposed to spending more to fight the virus, which has killed at least 11 people in the U.S. so far .

The bill, which includes more than $3 billion in vaccine research and $2.2 billion in prevention and preparedness efforts, far exceeds the $2.5 billion proposal that the White House put forward last week.

Only one senator, Republican Rand Paul of Kentucky, voted against the supplemental aid bill.

The Senate on Thursday passed a multibillion-dollar spending package to combat the spread of the deadly coronavirus. The bill will now head to the White House, where President Donald Trump is expected to sign it.

A House Democratic aide told CNBC that the supplemental funding bill includes:

More than $3 billion dedicated to the research and development of vaccines, as well as therapeutics and diagnostics;

$2.2 billion in public health funding to aid in prevention, preparedness and response efforts — including $950 million to support state and local agencies;

Nearly $1 billion to go toward medical supplies, health-care preparedness, Community Health Centers and medical surge capacity, and

$1.25 billion to address the coronavirus overseas.

Senate Majority Leader Mitch McConnell, R-Ky., and other lawmakers hope to push the legislation through to Trump before the week's end, stressing the urgency of securing funds to fight the virus.

Health officials have warned that the coronavirus is on the verge of becoming a pandemic, and a slew of new cases have been confirmed in the U.S. in recent days.

The disease, which is believed to have originated in Wuhan in China's Hubei province, has killed more than 3,200 people around the world and infected tens of thousands more, prompting wild market fluctuations and drastic government actions.

Senate Majority Whip John Thune, R-S.D., had suggested that the Senate might opt to pass the bill by unanimous consent in order to speed up the process. But McConnell's office confirmed to CNBC on Thursday morning that the Senate would hold a roll-call vote, requiring a 60-vote threshold for passage.

Paul, the only senator to vote against the bill, had put forward the only amendment to the legislation. Paul's amendment sought to offset the costs of the coronavirus spending by cutting funding for certain international programs.

"I support our government's efforts to fight the coronavirus," Paul said in a statement earlier Thursday. "We also owe it to the American people to do it in a way that avoids piling billions more in debt on their backs."

The Senate voted 80-16 to table — essentially, to kill — Paul's amendment prior to voting on the spending bill itself.

Paul's office did not immediately respond to CNBC's request for comment on the senator's decision to vote against the emergency coronavirus funds.

The spending plan also allows an estimated $7 billion in low-interest Small Business Administration loans to affected small businesses, the aide told CNBC.

The House aide added that the emergency bill provides more than $300 million to "help ensure that, when a vaccine is developed, Americans can receive it regardless of their ability to pay."

The question of affordability has reportedly been a sticking point in negotiations. Health and Human Services Secretary Alex Azar came under fire last week after declining to guarantee to lawmakers that a vaccine would be affordable for all.