Texans are grappling with a winter storm that has turned deadly as millions of people face freezing temperatures with no electricity — and no estimate for when they may get power and heat back.

At least 10 people have died as frigid temperatures pummeled the state over the long weekend. On Tuesday, local officials issued dire warnings that the blackouts were likely to continue.

"Whether you have power or not right now, there's a possibility of power outages even after today," Harris County Lina Hidalgo said during a press conference Tuesday. "I know things are bleak, and it's going to be a long week."

More than 3 million homes in the state were without power as of Tuesday evening, according to PowerOutage.us, which collects information on power outages. Coupled with the freezing temperatures, there has been a spike in carbon monoxide poisoning calls as people have resorted to using barbecue grills, generators, and even cars indoors as sources of heat.

In Harris County, Hidalgo said, officials have received at least 300 calls of carbon monoxide poisoning, including one regarding an 8-year-old girl and her mother, who passed out and died while on the phone.

"We're losing our family members to carbon monoxide poisoning," Harris County Fire Marshal Laurie Christensen said during the press conference.

The loss of heat has also resulted in frozen water pipes and contamination in some jurisdictions, prompting officials in the Rio Grande Valley and in Fort Worth to issue warnings to residents to boil water before use.

At least 10 deaths in the state are suspected of being connected to the cold temperatures.

In Sugar Land, a grandmother and three children on Tuesday were found dead after a house fire. Investigators told KHOU the cause of the fire was under investigation, but the family had been using their fireplace during power outages to try to keep warm.

In Houston, police said, a man whose body was found in a street median was believed to have died from exposure to the cold temperatures. Another 60-year-old man was found dead inside a van possibly from exposure.

Another man was killed on Monday after he was hit by a car on Interstate 10; he had just gotten out of his vehicle following a crash on the icy roads.

The Bexar County Sheriff's Office also told KSAT the death of a 78-year-old man, whose body was found in his home by his wife on Monday, may have been due to the extreme cold.

The number of fatalities related to the storm and cold temperatures may continue to rise.

In Galveston County, the medical examiner's office had requested on Tuesday a refrigerated truck to handle a surge of deaths as the county braces for even more icy rain, according to ABC 13.

It was unclear if that was directly connected to the storm, but Galveston County Judge Mark Henry told the local news station that the medical examiner's office needed to suddenly increase its capacity to hold an additional 20 to 50 bodies.

The county medical examiner's office also handles cases from neighboring Brazoria County.

On Tuesday, Henry blasted the state's electrical power grid, managed by the Electric Reliability Council of Texas (ERCOT), for the blackouts. In his county, most of the more than 340,000 residents have been without power for at least two days.

The county was told Sunday to prepare for rolling blackouts, but Henry said the situation had worsened since then.

"What we quickly found out was that they weren't rolling at all," he said in a Facebook post. "They went off and they stayed off for as much as 48 hours at this point, and counting."

He called the response "unacceptable," considering the storm had been anticipated for about a week.

The ongoing power outages have prompted officials to call for an investigation into the handling of the state's electrical grid. Unlike the rest of the US, most of Texas is on its own power grid, and its equipment could not withstand the freezing temperatures.

On Tuesday, Gov. Greg Abbott said he was calling for an investigation into ERCOT.

"Far too many Texans are without power and heat for their homes as our state faces freezing temperatures and severe winter weather," he said in a statement. "This is unacceptable."

Hidalgo in a press conference noted that the ERCOT had, throughout the weekend, issued optimistic messages that power would soon be restored, only for residents to face more long power outages.

She warned residents that until ERCOT's promises were fulfilled, they will need to continue to brace for cold temperatures and no power for the rest of the week.