Some bankers say they would prefer a more moderate candidate, and worry the Texas governor’s style and stances on social issues could sink him in the general election. Their unease, along with rules against governors accepting money from certain financial executives, could crimp Mr. Perry’s ability to tap into his party’s single biggest source of cash.

“Wall Street would only really go for him if they thought he could win—and they don’t,” said Rick Hohlt, a Washington lobbyist and Republican fund-raiser…

Others said Mr. Perry’s style is just as much a concern for Wall Street donors. “It’s the Texas bravado that rubs Wall Street the wrong way,” said Nathan Gonzales of the Rothenberg Political Report.

Complicating Mr. Perry’s pitch are changes to fund-raising rules that cap the amount some senior managers on Wall Street can give to state officials at just a few hundred dollars. A Securities and Exchange Commission rule that took effect earlier this year aims to prevent financial-sector donations from influencing regulators’ decisions on how to invest public pension funds. A 1994 rule also restricts Mr. Perry from raising cash from people involved in underwriting municipal bonds.