Gilberto Hinojosa, the chair of the Texas Democratic party, said Mr Abbot’s "lack of foresight and inability to manage this crisis is part of a repeated pattern,” in a statement on Wednesday.
The retort came as three million Texans were still without power supplies on Wednesday, after widespread blackouts across the state on Monday and Tuesday — caused by both a surge in demand, and supply issues with the state’s main power supplier, ERCOT.
As many as 21 people have died, with roads blocked and hospitals evacuated, amid other crises related to record breaking temperatures, which reached 0F (-18C) on Sunday.
"Crisis after crisis, Greg Abbott has failed and passed off blame to somebody else," said Mr Hinojosa. "Texas is in dire straits. Texans are dying.”
“Homes are being destroyed, people are cold and hungry, and we have no idea when things will begin to return to normal because our state government continues to fail,” said the Democrat.
“Millions of Texans are without power in freezing temperatures, many of them for the last 60 hours,” Mr Hinojosa continued. “At least 21 Texans have died. Their blood is on Abbott's hands."
The statement by Mr Hiojosa came after Mr Abbott said he did not when power supplies would return to almost three million Texans, and blamed ERCOT for being “opaque” about the four-day power outage.
"ERCOT has not provided information about which location and which geographic location the additional power is coming onto or is not coming on to," said Mr Abbott, who called on the energy supplier to be more “transparent”.
“ERCOT is an independent private entity that, candidly, I have both investigated, prosecuted before when I was the Attorney General of Texas. And we’re now investigating again,” Mr Abbott added.
Speaking on Tuesday, the Republican suggested that the state's wind and solar power sources were responsible for the blackouts, despite fossil fuels accounting for 80 to 90 per cent of Texas’s energy supplies.
“Our wind and our solar got shut down, and they were collectively more than 10 per cent of our power grid, and that thrust Texas into a situation where it was lacking power on a statewide basis,” Mr Abbot told Fox News.
Amid a backlash at those claims, the governor appeared to admit on Wednesday that “coal and natural gas power generating facilities either froze up or had mechanical failure and were incapable of adding power to the power grid.”
Beto O’Rourke, a former congressman and challenger to Republican senator Ted Cruz, told MSNBC News on Tuesday night that Texas was nearing a “failed state” due to Republican leadership.
The Democrat also wrote on Twitter that “Mr Abbott chose to ignore the facts, the science and the tough decisions and now Texans will once again pay the price”.
“If you can’t do your most important job — protecting the lives of those you were sworn to serve — then get out of the way and give the power and resources to local leaders who are fighting with all they’ve got to get past your mess and save the people in their communities,” Mr O’Rourke added.
Those remarks came as hospitals in Texas’s largest city, Austin, told the Austin Statesman that they were without power, affecting the transportation of patients and stopping toilet facilities from flushing, among wider issues.
Mr Abbott directed the state's gas producers to sell supplies to Texas’s power generators, in a bid to restart the wider supply grid, although cold temperatures are forecast for days still.
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