On Thursday and Friday, Mr Johnson blocked the bill from Republican senator Josh Hawley and progressive Democratic senator Bernie Sanders, which would have provided a second cheque of $1,200 to Americans, amid the ongoing coronavirus pandemic.
The first set of $1,200 cheques were provided to Americans who make less than $75,000 (£55,463) in March, as part of the first wave of coronavirus relief.
Mr Hawley, a senator for Missouri, attempted to get all senators to accept the bill on Thursday, as each representative needed to agree to it for it to pass through the Senate, according to The Hill.
Although cheques of around $600 (£443) are expected to be agreed by both Republicans and Democrats in the coming days, Mr Sanders and Mr Hawley have been pushing for them to be doubled.
“What I’m proposing will give working folks in my state and across this country a shot … at getting back up on their feet,” Mr Hawley told senators on Thursday.
However, Mr Johnson, a Wisconsin senator, objected to the bill and said: “I’m not heartless. I want to help people. I voted to help people. I voted for the $2.2 trillion (£1.6 trillion) CARES Act, but I also am concerned about our children’s future.”
He said that if the cheques are approved, then “we will not have learned the lessons from our very hurried, very rushed earlier relief packages,” as he cited the country’s increasing levels of debt.
Mr Johnson said that when it comes to coronavirus relief, “we all have compassion, we all want to fulfill those needs.”
However, he added that “one of the reasons we are $27.4 trillion (£24.8 trillion) in debt is we only speak about need, we only talk in terms of compassion.”
Mr Sanders, a Vermont senator, returned to the floor on Friday, but was unable to convince Mr Johnson to agree to the bill.
In order to get more time to agree on a new Covid-19 relief package, the US Congress and Senate passed a two-day stopgap spending bill on Friday.
The bill gives federal agencies funding until Sunday, to allow negotiators on both the Democratic and Republican sides to reach an agreement on a coronavirus relief package before the end of the year.
According to Johns Hopkins University, there are now more than 17.4 million people who have tested positive for the coronavirus in the US. The death toll has reached 313,672.