GE has been lobbying hard for Congress to reauthorize the Ex-Im Bank, maintaining it creates U.S. jobs. Much of the opposition to the bank comes from Republicans who maintain the bank inhibits the free-market economy by letting the government pick winners and losers. Some Democrats oppose it, maintaining it's a source of subsidies to big corporations.
"To me the logic for this is compelling," said Rice. "There are no other major countries that do not have export credit agencies, and through Congress' inaction the U.S is choosing to be the only one."
Rice said he could not say if GE was planning to move more jobs overseas because it no longer has access to financing from the Ex-Im Bank. He said it will be determined on a project-by-project basis, depending on the terms of the financing.
Read MoreGE continues to shed assets
In its statement, GE said, Congress' inability to reauthorize the Ex-Im Bank "will result in the loss of thousands of U.S. jobs—both at GE and at our suppliers."
The company is making the Ex-Im Bank an issue as it considers relocating its headquarters from Fairfield, Connecticut. A group reviewing potential sites is including the voting records of members of Congress on the Ex-Im Bank, as part of the criteria GE is using to make its final decision. Some states whose lawmakers opposed the reauthorization of the bank are no longer in the running.