Earlier on Monday, the Credit Union National Association (CUNA), said the legislation could come up during the lame-duck session and is needed to create jobs.
The bill would expand credit unions' lending authority to businesses to 27.5 percent of their assets, up from 12.25 percent. The CUNA argues that the change could help create more than 140,000 jobs.
"The tax-exempt credit union industry has sought to portray this legislation as a measure that is broadly supported throughout the credit union community," the letter said.
"Nothing could be further from the truth."
The letter cites a Government Accountability Office (GAO) report from January that showed "failed credit unions had more member business loans as a percentage of assets than peer credit unions that did not fail or the credit union industry."
"With growing opposition within the credit union industry and concerns raised by the GAO, Sen. Udall is now suggesting to combine this controversial legislation with unrelated banking legislation to move it through the Senate," it said.
"Any attempts to merge this permanent power grab legislation with a temporary extension of the current Transaction Account Guarantee (TAG) program or any other banking legislation will be strongly opposed by the banking industry."