(CNN) Congress is about to give the Small Business Administration hundreds of billions more in funding for the emergency small business lending program. But even amid growing outrage about some of the recipients so far, the guidelines for the loans aren't expected to change.

Even amid reports that dozens of public companies and well-known restaurant chains applied for, and received, money through the program, the Senate voted Tuesday for a proposal that increases the program by $310 billion without significantly overhauling the rules.

To some degree it illustrates a natural tension in attempting to craft an emergency program that kicks money out the door quickly, while also ensuring only a subset of businesses -- in this case, small businesses with fewer than 500 employees -- can qualify.

"The more requirements we came up with, the harder it was going to be to get the money out the door," Republican Sen. Marco Rubio of Florida, the lead writer of the program, said in a Tuesday interview on CNBC. "We erred on the side of expediency. The biggest mistake we can make is to move too slowly."

In this case that meant limiting paperwork for the application process as much as possible, according to people who helped draft the program, while setting the primary restriction as a certification that the business applying needs the money to maintain operations due to economic harm caused by the pandemic.

But as the initial funds were disbursed, banks -- concerned about their own regulations and rules -- gave preference to clients with whom they had preexisting relationships, and as such, detailed information about that company's eligibility, according to industry sources.

The new round of funding attempts to address this issue, at least in part, by including $60 billion in funds set aside for smaller lenders like community banks and credit unions to divvy out loans in hopes money trickles down to smaller businesses who may not have long-held existing relationships with a larger lender.

But there are no additional policy changes tied to the new money that would keep it from going to larger companies, including ones that are publicly held, that meet the eligibility requirements laid out by the law and Treasury Department.

Instead, lawmakers and policy makers are relying on public shaming as their only recourse.

"I know people who really enthusiastically (were) looking for $25,000, $30,000 loans, had all their ducks in a row, and the rest and just don't even get a response. That really has to stop. And Congress will be watching. You can be sure," House Speaker Nancy Pelosi said in an interview on MSNBC's "Morning Joe" on Wednesday.

While a handful of senators have raised concerns and frustrations about larger companies receiving the loans, behind the scenes, there has largely been broad, bipartisan agreement that franchise owners -- many of whom may own just one or a few franchises and employee just dozens of people -- should be eligible for the Paycheck Protection Program loans. And, larger, publicly-traded companies with fewer than 500 employees were also included to qualify for the loans with bipartisan agreement. In a testament to how widespread support for the program has been, on Tuesday when the Senate voted to include additional funding, the bill passed without a roll call vote even being called.

Right now, the only way Congress can stop well-known or publicly-traded companies from qualifying for the Paycheck Protection Program loans is to change the program's eligibility requirements. With members scattered across the country, finding broad agreement to change those rules is unlikely in the near term.

And while there was never a significant push to overhaul the application process, there was concern about what any significant changes could mean once the money was replenished, according to one bank executive.

"The roll out was tough enough -- with so much unclear about what we could and couldn't do," the executive said. "Now we feel like we have a good handle on things. Changing the rules now would only cause more delays and problems once that new money comes online."

Under the rules of the Small Business Administration's Paycheck Protection Program, businesses with fewer than 500 employees who self-certified that they were injured as a result of coronavirus could qualify. The program was designed broadly on purpose to assure that businesses could get money quickly. But, it wasn't a violation of the rules for larger and even publicly-traded companies to get the funding. Instead, it is only a violation if a business owner falsely self-certified on their application that coronavirus had made it hard for them to continue operating their business,

Sen. Rick Scott, a Florida Republican, called for that language specifically to be strengthened.

"We cannot throw caution to the wind in the middle of a crisis," Scott said. "We still have to be smart about how we spend taxpayer dollars."

But that effort did not make it into the new legislation, despite the bipartisan concern over some of the companies that have received funds, as it was determined the current language had a similar effect.

Treasury Secretary Steven Mnuchin said Tuesday that he planned to conduct oversight to ensure that businesses who received the loans were in need, but that could prove harder to do than say. Mnuchin said that Treasury will put out clear guidance explaining the rules of the self-certification and give business owners an opportunity to return the money if they violated the rules with no questions asked in the short term. However, Mnuchin promised "there are severe consequences for people who don't test properly to this certification."

He added that "we want to make sure this money is available to small businesses that need it, people who have invested their entire life savings. We appreciate what's going on and they're hiring people back."

Rubio, who is the chairman of the Senate Small Business Committee has also pledged to conduct vigorous oversight if a business owner who wasn't actually injured as a result of coronavirus received an SBA loan.

"Any business, regardless of size, must certify it has been harmed by the coronavirus crisis and that PPP is necessary to maintain operations," Rubio wrote Monday. "This fall, the Senate Committee on Small Business and Entrepreneurship will conduct aggressive oversight into the use of the PPP. If companies are not forthcoming, the Committee will use its subpoena power to compel cooperation."

Rep. Nydia Velazquez, the New York Democrat who leads the House Small Business Committee, has pledged similar oversight and will hold a hearing Thursday on the program's rollout.