The White House and Senate leaders reached a deal early Wednesday on a massive $2 trillion relief bill — said to be the largest rescue package in American history — to combat the economic impact of the coronavirus outbreak.

As of Wednesday morning, though, the Senate was still drafting the final details of the text. A senior Democratic aide told CNBC that due to procedural reasons, including how long it is taking the Senate to send over a draft of the bill, it is unlikely the House will vote on it Wednesday. The House needs to pass the bill before it can reach President Donald Trump's desk.

Efforts to pass the measure have taken on urgency as hospitals, companies, states and individuals have all pleaded for needed resources to battle the pandemic. Its impact has now reached into the Senate: Sen. Rand Paul, R-Ky., earlier this week announced he has tested positive for coronavirus.

"The Senate is going to stand together, act together and pass this historic relief package today," Senate Majority Leader Mitch McConnell said Wednesday afternoon.

In announcing the deal early Wednesday morning, the Kentucky Republican called the proposal is effectively "a war-time level of investment in our nation." He promised the bill would rush financial assistance to Americans through direct checks to households, enhanced unemployment insurance, hundreds of billions of dollars in emergency loans to small businesses, and more resources for hospitals and medical equipment.

The Senate has yet to release the final terms of the deal. An earlier draft seen Tuesday would provide cash payments of up to $1,200 for individuals, $2,400 for married couples and $500 per child, reduced if an individual makes more than $75,000 or a couple makes more than $150,000.

The draft language also stipulated a $350 billion fund for small businesses to mitigate layoffs and support payroll.

Employers will get a deferral of payroll taxes, and pay them back on a staggered basis in the coming years, the administration official said. The deferral only applies to employers, and not employees.

McConnell said the bill would "stabilize key national industries" to prevent as many layoffs as possible, likely referring in part aid the deal allocates to the U.S. airline industry. The industry employs some 750,000 people.

Carriers have been racing to cut costs, grounding hundreds of planes and asking thousands of workers to take unpaid leave. Airlines are also tapping credit lines to shore up cash to weather the crisis, the impact of which they say is worse than 9/11.

The details of airline aid was one of the last major outstanding issues Tuesday night. Airlines have pushed for half their aid in grants, warning that receiving it entirely in loans would load them with too much debt.

Senators on Wednesday were moving ahead with $60 billion in aid for the beleaguered airline industry. That included $25 billion in direct cash grants for passenger carriers, $4 billion for cargo airlines and $3 billion for airline contractors, such as catering workers, in exchange for their employers agreeing not to furlough workers through the end of September.

The rest of the aid will be in form of loans with warrant provisions.

According to the draft language, which still may change, airlines have agreed to limits on executive compensation as part of taking on federal aid. They will be barred from stock buybacks while receiving assistance, and from providing stock dividends for a year after the bailout.