MADISON, Wis. — As Gov. Scott Walker prepares to announce his campaign for president next month, promising to bring what he calls “big bold leadership” to Washington, as he did in Wisconsin, he faces a cloud over that story line: Republicans back home are in revolt.

Leaders of Mr. Walker’s party, which controls the Legislature, are balking at his demands for the state’s budget. Critics say the governor’s spending blueprint is aimed more at appealing to conservatives in early-voting states like Iowa than doing what is best for Wisconsin.

Lawmakers are stymied over how to pay for road and bridge repairs without raising taxes or fees, which Mr. Walker has ruled out.

The governor’s fellow Republicans rejected his proposal to borrow $1.3 billion for the roadwork, arguing that adding to the state’s debt is irresponsible.