Following G.E., Boeing announced on Tuesday that it had lost a bid to sell satellites to a Singapore-based satellite operator, Kacific, because the aerospace giant did not have the backing of a governmental export-credit agency. This news came two months after Boeing similarly lost a contract with Bermuda-based ABS Holding Ltd. and said it would be reducing the work force in its satellite manufacturing business, in part because of uncertainty over the Ex-Im Bank.

The developments came as lawmakers drifted back from their long summer recess, and bank advocates searched for a legislative way to reopen the agency. The hope is to add language renewing its charter to one of the many bills Congress must pass this fall, perhaps one to finance the government or a transportation measure. Without renewal, the bank is open only to manage existing credit and insurance business for foreign deals.

More than 100 chief executives for corporations who are members of the Business Roundtable arrived in Washington on Tuesday for an annual meeting, a day after the group’s chairman sent congressional leaders a letter urging extension of the export credit agency. On Wednesday the group will meet with President Obama, who, along with most Democrats, supports the bank.

On this issue among others — like funding the government, raising the federal borrowing limit and financing highways — such business groups have found themselves at odds with traditional Republican allies who increasingly reflect a new populist strain of conservatism in the party that is often hostile toward big business. For decades, the Ex-Im Bank was reauthorized by bipartisan votes, often unanimously.

The National Association of Manufacturers recently stopped hosting the fund-raisers at its well-appointed offices that drew business donors for Republicans. Boeing and G.E. have not explicitly vowed to withhold support, but Boeing’s vice president of communications, Gordon Johndroe, a former aide in the George W. Bush administration, said, “It would be odd for us to hold a fund-raiser or make a large contribution to someone who’s being vocally opposed to an issue of such importance to us.”

The bank’s opponents are “in some cases economically illiterate,” said John Engler, the president of the Business Roundtable and a former Republican governor of Michigan. “I think it’s the antigovernment nature of so many members” elected since the Tea Party’s rise in 2010, he added. “It’s inexplicable. Texas is the largest beneficiary of the Ex-Im Bank. We had in the last year 3,700 transactions that involved the bank, 164,000 jobs.”

Mr. Bennett, the head of the manufacturers group in Republican-controlled Texas, said that at all levels of government, “the ultra-right wing of the party has put a fear factor into our elected officials, and we see some very bizarre behavior, very anti-business behavior and rhetoric out of these folks.”