Senate Majority Leader Mitch McConnell has yet to schedule a Senate vote to pass the country's second emergency coronavirus deal after the House passed the package early Saturday morning.

The Democrat-led House last week passed the second round of legislation, which was aimed at helping workers and individuals struggling to make it through the crisis. Among the provisions agreed to between Treasury Secretary Steven Mnuchin and House Speaker Nancy Pelosi were increased unemployment insurance and paid sick leave.

Deal talks between the Trump administration and the House went late into the night Friday, and Mnuchin said Saturday the two have agreed to issue a "technical correction" to the bill on Monday. That means the Senate does not yet have a bill to vote on.

Paid sick leave has become an issue for at least some Republicans.

Democrats and the White House pushed for paid sick leave, because it allows workers who are sick or quarantined the ability to stay home without losing their paycheck. Some Republicans worry about its cost to businesses.

"Although mandating that all employers must pay for sick leave might sound good, we need to consider the unintended consequences of this legislation," said Republican Sen. Ron Johnson of Wisconsin in a statement after the House bill passed.

"I fear that rather than offering a workable solution, the House bill will exacerbate the problem by forcing small businesses to pay wages they cannot afford and 'helping' them go further into debt," Johnson said.

At a press conference Saturday, Mnuchin said the deal struck with the House offers certain exceptions for smaller companies that may not have the funds to cover workers forced to stay home.

"We were also very sensitive to small- and medium-sized businesses. Many of these businesses cover sick pay, but they're going to have many more people that may be on quarantine, and we didn't want them to cover the cost," he said. "So 100% of the cost for these limited situations will be taken care of by the federal government."

In a statement on Monday, McConnell said the Senate had yet to receive the final House version of the bill.

"First, we still need to receive the final version of the House's coronavirus relief legislation," he said. "I commend Sec. Mnuchin for his hard work on this. I know Senators on both sides are carefully reviewing the details and are eager to act swiftly to help American workers, families and small businesses navigate this challenging time."

The next vote the Republican-led Senate has scheduled is over the renewal of national security surveillance law, Foreign Intelligence Surveillance Act, or FISA. That is scheduled for Monday at 5:30 p.m.

"Until the FISA legislation is passed, any action on the House coronavirus legislation will take unanimous consent," a spokesperson for McConnell told CNBC.