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Small business owners are finding that days after forgivable loans were supposed to be made available under the CARES Act coronavirus stimulus package, several large financial institutions are either not accepting applications or placing specific restrictions on who can and cannot apply.

The Trump administration announced that loans would be available beginning Friday, April 3, but as of Wednesday morning, Citibank was still not accepting applications from customers. JPMorgan Chase’s system was down until Monday afternoon. As President Trump addressed the possibility that the roughly $350 billion allotted for the loans may not be enough, many customers may be at risk of being shut out as they wait for their banks to open the application process.

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“I will immediately ask Congress for more money to support small businesses under the #PPPloan if the allocated money runs out,” Trump tweeted over the weekend, vowing to help business owners unable to secure loans in time.

Lawmakers on both sides of the aisle are now looking to pump billions more into the Small Business Administration program.

In the meantime, confusion has increased as individual banks have seemingly given mixed messages as to their participation in the loan program.

Several small business owners told Fox Business when the application process began that the program is suffering from a series of defects and that loan applications were being summarily rejected for arbitrary reasons. Others said they were getting the brush-off from their bankers who had said Friday they did not have guidance from the federal government to begin the application process.

Citibank confirmed to Fox News on Friday that they are "reviewing the new SBA guidelines and we expect to begin accepting online loan applications as soon as possible," but as of Wednesday morning their website still said that while they are participating in the program they “are not yet able to accept applications.”

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Similarly, JPMorgan Chase’s online application system had been down with a note stating it would “be back up shortly,” finally announcing Monday afternoon that customers can now apply online. The website still notes that “[f]unds are limited and subject to availability from the SBA," cautioning customers that they may not end up getting what they are hoping for.

Wells Fargo customers are already out of luck if they did not apply between Friday and Sunday. The bank, which said they were focusing on "nonprofits and small businesses with fewer than 50 employees," announced that their application process was up and running but that demand was so high they stopped taking new applications, reviewing only those received through April 5.

“Given the exceptionally high volume of requests we have already received, we will not be able to accept any additional requests for a loan through the Paycheck Protection Program,” a statement on their website said. The bank noted that they expect to distribute $10 billion in loans.

Trump credited local banks for accepting loan applications on schedule. He also praised Bank of America, even though they came under fire for how they limited who could apply for a loan. Initially, customers had to have a business relationship with the bank and hold a credit card there. After complaints, they eased restrictions to allow customers with individual or business accounts, as long as they did not have business or credit relationships with another bank.

Other banks such as TD Bank and PNC are accepting applications, but only from customers with business accounts.

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Treasury Secretary Steven Mnuchin said more lenders would be available this week, and SBA Administrator Jovita Carranza announced over the weekend that the agency has “reactivated 30,000 licenses for community banks and credit unions” so that more businesses can get money.

The SBA has also provided a tool for business owners to search for lenders.

As those who have been able to apply for loans are swiftly depleting the designated funds, Senate Majority Leader Mitch McConnell, R-Ky., expressed the need for additional money to be made available.

"Jobs are literally being saved as we speak. But it is quickly becoming clear that Congress will need to provide more funding or this crucial program may run dry," McConnell said in a statement. "That cannot happen."

Mnuchin then announced Tuesday afternoon that he spoke with McConnell, Senate Minority Leader Chuck Schumer, House Speaker Nancy Pelosi, and House Minority Leader Kevin McCarthy, R-Calif., to secure $250 billion in additional funding.

On Wednesday, Pelosi and Schumer included the small business funds as part of a proposal worth over $500 billion to extend additional coronavirus relief.

Fox Business’ Charlie Gasparino and Lydia Moynihan contributed to this report.