The tight spending plan calls for nearly level funding for most agencies.
Prisons Commissioner Kim Thomas said the spending plan underfunds his agency and will make it difficult to improve problems with care of female inmates or upgrade women's facilities.
But House Speaker Mike Hubbard said, "We don't have enough money to fund everybody's needs."
The General Fund budget will be on the agenda in the House on Tuesday. Hubbard said Friday that the House has adopted a calendar that will allow for several days of debate on the spending plan for most non-education state agencies.
He said he expect the Legislature to mostly wrap up work on both budgets by the end of the week or early next week.
"Our goal is to get it done earlier than in the past," Hubbard said.