WASHINGTON — With no serious negotiations in sight, a disorderly and divided Congress slipped closer to a double-barreled fiscal crisis on Thursday as House Republican leaders tried to shift the budget dispute to a fight over raising the government’s borrowing limit.

Trying to round up votes from a reluctant rank and file, House Republicans said they would agree to increase the debt limit to avert a mid-October default only if Democrats accepted a list of Republican priorities, including a one-year delay of the health care law, a tax overhaul and a broad rollback of environmental regulations.

At the same time, Speaker John A. Boehner of Ohio signaled he was not ready to abandon a spending fight that could shut down the federal government as soon as Tuesday. Asked whether he would put a stopgap spending bill to a vote free of Republican policy prescriptions, he answered, “I do not see that happening.”

President Obama, who has faced three years of down-to-the-wire standoffs that have nearly ended in default or shutdowns a half-dozen times, fired back with a broadside of his own.