Senate Majority Leader Mitch McConnell's plan to move at "warp speed" to pass an emergency coronavirus bill hit a familiar bump on Tuesday night: Senator Rand Paul, his fellow Kentuckian.

The GOP leader had teed up a measure sent over by the House that would provide free coronavirus testing, paid leave for some workers, beefed up unemployment insurance, and enhancements to food security and Medicaid programs.

Mr McConnell acknowledged Tuesday that some in his caucus are frustrated with the House-passed bill, seeing "considerable shortcomings." In an attempt to garner more Republican votes for a crisis that has slowed much of normal American life, the Senate GOP offered his caucus some advice.

"My counsel to them is to gag and vote for it," he said.

It appeared most would do just that Tuesday, until Mr Paul, as he often does, put up one last speed bump.

Mr Paul dashed Mr McConnell's plans by offering an amendment to the House-passed bill that reportedly would "require a social security number for purposes of the child tax credit, and to provide the President the authority to transfer funds as necessary, and to terminate United States military operations and reconstruction activities in Afghanistan."

That amendment is expected to fail in what has become something of a Washington ritual.

Mr Paul often waits until the eleventh hour to offer an amendment to a major legislation. Knowing he lacks the vote, he grabs the spotlight -- and headlines -- to make a point. Mr McConnell, eager to move to a final vote on that major bill, allows the amendment debate and vote and essentially lets his Kentucky delegation mate vent some steam.

That second emergency virus measure the Senate could take up and pass as early as Wednesday would come before votes perhaps later this week on a massive economic stimulus measure to counter the coronavirus, which some analysts say could leave millions jobless by this summer.

The service industry is expected to lay off scores of hourly workers, and the US stock markets, despite gains Tuesday, have been losing value for the last two weeks.

Treasury Secretary Steven Mnuchin and Speaker Nancy Pelosi have been leading discussions about that stimulus bill, with no signs that sizeable blocs of either party plan to block what sources say could be a bill as large as $850bn -- larger even than the annual Pentagon budget.

"We're able to rise above our normal partisanship and many times our normal positions because these are not ordinary times. This is not an ordinary time," Mr McConnell said Tuesday.

His comments came amid a report that Mr Mnuchin warned senior lawmakers that some administration projections showed unemployment possibly hitting 20 per cent at the peak of the outbreak crisis. But top White House aides are disputing that report.