The devastating hurricane made landfall in the state a week ago and has been blamed for at least 47 deaths. About 43,000 people are being housed in shelters.
The US government has already asked Congress for $7.85bn as an initial contribution towards recovery efforts, which Mr Abbott called a “down payment”.
Abott told Fox News. that judging by the number of homes and business affected by this disaster he estimates that costs will be between $150bn to $180bn,
The White House has warned that the US debt ceiling – the cap on government spending – will need to be raised to meet the bill for recovery. Only Congress can raise that limit.
While the rain has shifted away from Houston, the US’s fourth largest city, much remains underwater. The state of Texas is one of the US’s main economic engines.
The storm struck at the heart of America’s oil and gas industry, knocking a third of all US production offline, closing refineries around the Gulf Coast, and causing major pipelines that move fuel to other markets to shut.
Gasoline prices which increased in anticipation of the storm, are expected to continue to rise, despite additional shipments from overseas.
The Houston region is responsible for more than $500bn in economic activity annually.
AccuWeather expects the storm to shave a full percentage point off US GDP over 12 months and lead the Federal Reserve to hold off on raising interest rates.