The top Democrat and Republican in the US Senate joined forces in a rare moment of unity on Thursday in an attempt to pass $40bn in aid for Ukraine, only to be stymied by a single Republican lawmaker: the Kentucky libertarian Rand Paul.

Faced with the prospect of an extended delay for the package that passed the House of Representatives on Tuesday, the Senate majority leader, Chuck Schumer, and his Republican counterpart, Mitch McConnell, sought to move forward on the aid package only to be blocked by Paul, a fiscal hawk who objects to the amount of spending proposed.

The stalemate delayed passage of the measure into next week.

The Senate has scheduled an initial procedural vote on the bill for late Monday afternoon.

It was unclear whether that vote would then speed passage of the Ukraine aid. Alternatively, passage could come around the middle of next week if any senator wants to force a series of legislative steps before a final vote.

As the Ukraine aid bill became caught in the Senate’s procedural gears, Schumer pleaded for fast action: “The package is ready to go, the vast majority of senators on both sides of the aisle want it.”

He added: “If Senator Paul persists in his reckless demands … all he will accomplish is to single-handedly delay desperately needed Ukraine aid.”

But Paul was not moved.

The delay into next week could cause problems for western countries trying to bolster Ukraine in its fight against Russia.

The Biden administration has said that by 19 May it expects to run out of available funds to draw on under an authority that allows the president to authorize the transfer of weapons without congressional approval in response to an emergency.

Paul is demanding that the legislation be altered to require an inspector general to oversee spending on Ukraine. Without his agreement, the Senate must follow a lengthy process stipulated by the chamber’s arcane rules.

McConnell, Paul’s fellow senator from Kentucky, weighed in, saying: “Ukraine is not asking us to fight this war. They’re only asking for the resources they need to defend themselves against this deranged invasion. And they need this help right now.”

The House passed the Ukraine spending bill by 368 to 57, with only Republicans voting against it.

Joe Biden had asked Congress to approve an additional $33bn in aid for Ukraine. But lawmakers decided to increase the military and humanitarian funding.

“This is the second spending bill for Ukraine in two months. And this bill is three times larger than the first,” Paul said before formally blocking the aid package. “Congress just wants to keep on spending, and spending.”

The aid package had previously included more spending for dealing with Covid-19 in the US, but the two causes were decoupled after Republicans balked.

Meanwhile, the White House Covid-19 coordinator, Ashish Jha, issued a dire warning that the US will be increasingly vulnerable to the coronavirus this fall and winter if Congress does not swiftly approve new funding for more vaccines and treatments.

In an Associated Press interview, Jha said Americans’ immune protection from the virus was waning, the virus was adapting to be more contagious and booster doses for most people would be necessary, with the potential for enhanced protection from a new generation of shots.

His warning came as the White House said there could be up to 100m infections from the virus later this year and as Biden somberly ordered flags to half-staff to mark the imminent milestone of 1 million US Covid deaths.