STAMFORD — Stamford Health’s COVID-19 clinic is already doling out between 700 and 900 doses primarily of the Moderna and Pfizer vaccine on weekdays. On weekends, that number climbs as high as 1,200, according to Stamford Health officials.

But the shared goal of the hospital, the city and legislature is to continue increasing that capacity and get more shots in arms. That ramping up in distribution will be, in part, supported by federal aid from the American Rescue Plan Act, a $1.9 trillion stimulus package that would send direct aid to individuals, cities and states.

Sen. Chris Murphy, D-Conn., was a proponent of the bill, which passed the Senate this weekend and is awaiting approval from the House of Representatives and ratification from President Joseph R. Biden. Both of those approvals could happen this week, Murphy said Tuesday morning, on a tour of Stamford Health’s vaccination clinic, where he was joined by Mayor David Martin, Stamford Health Chief Operating Officer Jonathan Bailey and Chief of Infectious Disease Michael Parry, among other hospital staff.

“Obviously, the issues right now are simply supply,” Murphy said, standing outside of Stamford Hospital’s Wheeler Building, a formerly decommissioned part of the hospital complex that was re-purposed during the pandemic. “We need to produce more vaccine. Stamford has the ability to distribute more. We need to get more into the city and into the state.”

According to Murphy, the bill includes funding for increased vaccine production and distribution, as well as money for existing clinics to expand as more doses become available. The total amount of vaccine in Connecticut, Murphy said, would likely be greatly increased by April. And Parry said the hospital and city, which have partnered in the distribution of the vaccine, are looking to open a second, more capacious facility in Stamford’s South End.

But for now, Parry said the Wheeler Building has served its purpose as a vaccination hub in the city.

Patients enter the building through a tented-off section near the hospital’s Emergency Department. They’re checked-in on the first floor, then go to the second floor, the south side of which is a designated vaccination area, Parry said. After receiving a dose, patients then move to the north side of the building, where they are observed for a brief period and appointments for a second shot are scheduled.

Generally, Parry said, people are in and out within 30 minutes.

“It really is a very logical flow,” Parry said.

The same is true for teachers, for whom the city, hospital and public school district have organized large clinics, the first of which was held over the weekend. Additional educator clinics are scheduled for weekends through the end of the month, in an attempt to get all teachers and school staff at least their first dose of the vaccine by March 31. According to Martin, the city is on pace to hit that target.

In order to keep up with demand — especially since March 1, when educators and residents over age 55 became eligible — Bailey said the hospital had hired more than 200 people to staff the clinic, which operates seven days a week from 7 a.m. to 7 p.m.

Murphy was visiting to thank the hospital staff that enabled the clinic to function, as well as to discuss the American Rescue Plan Act, which he said would have a direct impact of Connecticut and Stamford residents.

The plan would extend the Paycheck Protection Program Loan, potentially helping hundreds of small businesses in Stamford, Murphy said. It would enable low-income families with kids to qualify for an extended child-tax credit and would expand unemployment benefit programs. Stamford Schools will receive millions from the bill to aid in reopening. And, it includes an additional $1,400 rescue check for individuals making under $75,000 a year, which Murphy said could start being distributed in the next two weeks.

“The economic assistance in this bill is especially important in a high-cost part of the country like Fairfield County,” Murphy said.

In total, Stamford is expected to receive just shy of $50 million in aid from the legislation — a crucially important boost for the city, Martin said.

“I believe that the city of Stamford’s economic recovery will be very strong in large part to the American Rescue Plan,” Martin said. “Not only the aid but the certainty of the aid which is now coming to fruition. And yes, it’s helping with a lot of people at the low end of the economic spectrum, but it’s also helping with the schools and the city and how we’ve struggled through this pandemic, both from the health side as well as from an economic side.”