Friday is the deadline for Congress to act before automatic spending cuts will take place. Cuts that are on the table include national defense, insurance and education.
Some economists said the automatic cuts could raise the national unemployment rate by 1.5 percentage points.
Texas would lose almost $68 million in funding for primary and secondary education.
Head Start and Early Head Start programs that are almost 100 percent government funded could be hit the hardest.
"It's extremely frightening. It's the kind of thing that keeps me awake at night because I know what we do for kids and parents is really, really important," said Cheryl Cunningham, the director of early childhood programs at Woodson Early Head Start School in Abilene.
Sequestration could cut about 5,000 Texas children from the program, about 7.5 percent of the 67,000 across the state.
"If our budget is cut, it comes directly right back to people and the jobs that we have serving the kiddos and it would be devastating," said Cunningham.
"The federal law mandates that we can only have 20 children in a classroom and you have to have one adult for every ten children and so if you cut staff you cut kids," she added.
Some economists predict more than 160,000 jobs will be lost in Texas if sequestration takes place on Friday.
On the defense side, about 52,000 jobs would be furloughed in the Lone Star State. The Air Force in Texas could see $27 million in cuts.
Also, about 2 percent of federal Medicare funding will be lost.
However, there are some programs that are exempt from sequestration. Some of those include Medicaid, Children's Health Insurance Program and Social Security.