"It's going to cause us problems if we're going to have to go babysit these depositions, because we simply don't have the resources," Caldwell said.
CNSI attorney Lewis Unglesby replied, "I don't see in the code of civil or criminal procedure 'overworked' as an excuse."
Kelley said Caldwell filed no evidence to suggest that allowing the wrongful termination lawsuit to proceed would harm the criminal case.
"I just don't believe that there's been a showing made of the need for a stay at this time," he said.
Caldwell suggested it was unlikely he would appeal Thursday's decision.
The Jindal administration scrapped the 10-year Medicaid claims processing contract with CNSI on March 21, after details emerged about a federal subpoena seeking information about the contract award. The attorney general's office empaneled its own grand jury on May 23 to look into possible criminal activity.
The Jindal administration has accused its former health secretary, Bruce Greenstein, of inappropriate contact with CNSI throughout the bid process. Greenstein, a former CNSI vice president, resigned a week after the company's contract was terminated, but he has denied involvement in the contract award.
CNSI sued the Jindal administration in response to its firing, saying it did nothing wrong.
Only one deposition has taken place during the legal wrangling over the case since it was filed: a nine-hour questioning of Greenstein last week.
Kelley said the attorney general's office had "gained the benefit of an effective stay" from May until November, which was longer than the original delay request that Caldwell had sought.
The attorney general's office has said it was concerned that CNSI would try to tamper with witnesses in the criminal investigation by using information gained through its civil lawsuit against the state.
Caldwell has pointed to a now-closed FBI case in Maryland in which CNSI owners were accused of threatening to kill a witness. But CNSI attorney Lewis Unglesby said the accusations have been discredited and no charges were filed. The case was closed in 2011.
Caldwell said the closing of the case doesn't mean the accusations weren't true, but he also didn't seek to enter the FBI documents into evidence Thursday and Kelley said he, therefore, couldn't consider them.
