AUSTIN, Texas (NEXSTAR) — Robert Dragisic is encouraged by the development of the COVID-19 vaccine, though he — like many Texans — is having trouble getting access to the shots.

“We should be able to get it,” he said.

Texas Lt. Gov. Dan Patrick suggests shifting perceptions.

He wrote a letter to the chair of the Expert Vaccine Allocation Panel — the state group making rollout recommendations — saying he wants Texas to create some subgroups within the Phase 1B priority group “…so that the more than 4 million-plus Texans and those with chronic conditions don’t all expect to get their vaccination at the same time — something we know is not possible.”

“Texans need to have a better understanding of the time it will take for everyone to be vaccinated in order to reduce lines, confusion and frustration,” Patrick explained.

Patrick’s plan includes first vaccinating Texans 75 and over, which might “cut down on long wait times and begin to address the most vulnerable.” Patrick said there are less than 1.5 million people in that group — some in nursing homes. After that, Patrick suggested vaccinating all teachers and school staff over 65, a group of fewer than 60,000 people, he said. Then, communities will be better able to handle the remainder of Phase 1B, broken down even further into smaller groups by odd/even birth year, month or day.

“Too many Texans are spending long days physically standing in line, calling a phone number repeatedly, and spending hours online, trying in vain to get a vaccination appointment,” Patrick wrote.

“Demand clearly outstrips supply,” he continued. “While conditions do differ across the state, available appointments are often hard to find and they disappear quickly.”

The concerns for the state’s vaccine rollout span across both chambers of the Capitol and both major parties. Beyond the letter from Patrick, who presides over the Texas Senate, a bipartisan group of lawmakers from north Texas, including House Democrats and a Republican and State Sen. Royce West, D-Dallas, wrote to Commissioner of the Texas Department of State Health Services, Dr. John Hellerstedt on Thursday, asking for additional vaccine hubs in the region.

“The residents of Irving and Grand Prairie are, we believe, best served by placing a vaccine hub within the corporate limits of either city for Week 7 and Week 8 of vaccine distribution,” they wrote.

State Rep. Terry Meza, D-Irving, says some of her constituents have transportation trouble getting to the existing hubs in Dallas and Tarrant Counties.

“Eligibility doesn’t equate to availability,” she said.

A spokesperson from the Texas DSHS said Friday it is up to existing hubs to ensure accessible locations for their populations.

“Hubs are not placed in a specific location by DSHS,” agency spokesperson Lara Anton wrote in an email. “Providers who can operate a vaccination hub are allocated a larger amount of vaccine with the expectation that they will use all of the doses within a week, vaccinate everyone eligible and they will target the hardest-hit zip codes and demographics.”

“A hub provider doesn’t have to remain in the same location or even be in just one location,” Anton continued. “A hub provider could split their allocation between multiple locations to ensure that they provide easier access to people in different parts of the county.”

“There are several hub providers in Tarrant County that local officials could work with to set up a vaccine clinic in those cities,” Anton stated.

Anton mentioned the supply of vaccines is limited by the ability of the manufacturers to produce them as well as the amount allotted to the state by the federal government.

“The federal government determines how much vaccine will be sent to Texas on weekly basis,” she explained.

According to state data released Friday, 0.81% of Texans (228,314) are fully vaccinated, and 5.10% (1,144,166) are partially vaccinated.

Ed Zavala and Frank Jefferson contributed to this report.