The court on Tuesday will consider whether to ask voters in November to approve a massive bond package that could range from $970 million to $1.5 billion.
The Port of Houston Authority has requested up to $550 million of that for ongoing construction of its Bayport Container and Cruise terminal, and for security and environmental initiatives.
On Tuesday, the Commissioners Court will have before it five options outlined by the county's Office of Budget and Management Services.
The options include different amounts proposed for the port and other projects, such as roads, parks, an inmate processing center, juvenile facilities, a new family law center and a new forensic center.
"I think what we will end up doing is looking at what our tax base will allow us to do and work backward from there," Harris County Judge Ed Emmett said Friday.
"It will require us to set priorities, and that is something that the entire court gets to do."
The five outlined options would require property tax rate increases of 1.8 to 2.8 cents per $100 assessed value, according to the county budget office.
But Emmett and several commissioners said they do not want to seek a tax rate increase to pay for the bond package.
The county's ad valorem rate of 63.99 cents per $100 assessed value has remained unchanged for six years.
"For us, it's critical that we really look at making sure that we don't raise taxes and that we don't add any additional burdens to the property taxpayers," Commissioner Sylvia Garcia said.
The options outlined by the county budget office range from a total of $970 million to more than $1.5 billion.
The court could select any one of the options or craft its own.
"You have to look at how much you bite off and how much you can afford to put off," Commissioner El Franco Lee said. "All those considerations are wrapped into what we decide to do."