The $600 stimulus checks have been deemed an "insult" and a "joke" by critics on Twitter.
The second stimulus check is worth half the amount of the first check that was paid to qualifying Americans earlier this year.
A Democratic lawmaker said a "principled stand" from progressives secured a second round of direct checks.
The Senate's vote to fill the gap happened just a few hours before the deadline for a nearly $1 trillion stimulus bill that could help Americans just days before Christmas.
Top Republican senators have sent mixed signals on whether it would get done with just hours before the deadline.
Lawmakers may need to again approve a stopgap spending measure to avoid a government shutdown as they finalize a nearly $1 trillion relief package.
"Without state and local funding, the vaccine distribution will be delayed. You will be held accountable for that delay, which will lead to more deaths and make the federal vaccine program a debacle," the New York governor wrote in a letter to the president.
Democrat and Republican negotiators are said to be closing in on a new package, but there remains some uncertainty over the eligibility for direct payments.
Democrats charge the provision is an attempt to impede President-elect Joe Biden's incoming administration.
Ron Johnson said Friday "I want to help people" but COVID relief efforts need to be "more targeted."
Congressional debate over the pending $900 billion COVID-19 relief bill again underscores the split between Democrats and Republicans over who should receive the funds and how the money can best be used.
In a tweet on Friday, New York Rep. Alexandria Ocasio-Cortez criticized Republicans for "demanding corporate immunity for worker abuse AND tax cuts for the very rich AND subsidies for friends AND total lack of oversight or accountability for their connected pals scamming PPP."
"I'm even more optimistic now than I was last night that a bipartisan bicameral framework for a major rescue package is very close at hand," the Senate majority leader said Friday.
The objection to Sen. Josh Hawley (R-Mo.) trying to pass more direct payments was expected, but it underscored the tensions surrounding more coronavirus relief as congressional leaders have yet to reach an agreement over a nearly $1 trillion package.
The Republican senator said the U.S. should not "borrow any money" as he hit out against stimulus proposals.
Discussions over a further relief package have been described as productive, with speculation having mounted that a further round of direct payments will be included in any such deal.
The Democratic representative said the checks would be "hardly sufficient" if included in the next COVID-19 relief bill.
Passing another stopgap spending bill could keep the government open past a Friday night deadline while congressional leaders iron out their differences over a $900 billion package. However, resistance is expected.
The Federal Reserve plans to keep interest rates low for the foreseeable future, even if the economy recovers sooner than expected from the COVID19 slump. The decision to keep interest rates low is good news for homebuyers shopping for a low mortgage rate, but bad news for small savers.
Leaders are more optimistic and closer to reaching a deal than they have been in the past nine months since the CARES Act passed in March.
"I think that is misguided and I don't think it's candidly very progressive," Senator Mark Warner said about the progressive's demands for a second round of stimulus checks.
Lawmakers are reportedly closing in on a package that would include $600 stimulus payments to most Americans, but it is much less than what most people want, according to recent polling.
Several people took to social media to express their disappointment with the amount of the latest stimulus check.
The package will be the first significant legislative response to the coronavirus pandemic since the CARES Act in March.
It is nearly nine months since the last relief package including Economic Impact Payments was signed off.
The Vermont senator said the proposals were "much too small" amid rising poverty and debt.
"The first wave was like a shotgun start and then a brick wall finish because the money ran out," O'Malley said of the first round of stimulus. "When a smaller amount gets made available this time, it's going to be another shotgun start."
Congress is close to a deal on a bipartisan stimulus plan, which is almost $900 billion short of what the president offered back in the fall.
"I don't understand the hesitation," the vice president-elect told "Good Morning America." "The people are suffering."