(NewsNation) — Over a dozen Republican senators threatened to delay a vote for the National Defense Authorization Act if the mandate requiring service members to get the COVID-19 vaccine does not get removed.

The act authorizes Department of Defense activities, appropriations and programs for the upcoming fiscal year.

So far, Sen. Rand Paul, (R-Ky.) said, 20 Senate Republicans have signed a letter saying they will vote against cloture on it over the COVID-19 vaccine mandate for military members, NewsNation partner The Hill reported. 41 votes are needed to block cloture, which needs to be invoked before the Senate votes on the bill.

The Pentagon began requiring COVID vaccines for all military in August of last year. About six months later, the Pentagon told Congress around 3,400 troops were dismissed for not following the mandate.

Republican governors and senators recently sent letters to congressional leadership, urging them to get rid of this mandate.

They argue the vaccine requirement could impact military readiness since it could force members to leave.

“The conflicts are getting worse, not better,” Sen. Lindsey Graham (R-S.C.) said. “We need more people in the military, not less, and this mandate is going to result in tens of thousands of able-bodied Americans who are well-trained leaving the military because they chose not to get vaccinated.”

Senators who signed onto the petition don’t only want to see the mandate eliminated — they would also like members who got discharged for not following it to be reinstated with back pay.

Matt Marecic, who was discharged from the Army for not getting the vaccine, also says it’s time for the mandate to end.

“It’s very emotional. I wanted to do that for my entire career,” he said. “They told us we were going to be punished for it but they didn’t tell us to what extent.”

Sophia Galdamez, one of seven Coast Guard Academy cadets disenrolled this past August, said she thought she would get a religious exemption from the vaccine.

“They gave us 24 hours to pack up — to leave the academy and get to our home addresses completely on our own,” she said.

Both the Biden administration and Pentagon continue to stand by the mandate. Last year, then-Pentagon Press Secretary John Kirby, who is now the spokesperson for the National Security Council, said the mandate is a readiness issue, and it helps protect service members from getting coronavirus.

“(Soldiers) do meet key national security needs, so it’s important for them to get these vaccines,” Kirby said.

When asked if the vaccine mandate is affecting military recruitment, current Pentagon press secretary Pat Ryder said Thursday that they aren’t drawing a correlation between the two.

“Certainly we continue to look broadly at how we can recruit and how we can attract recruits,” he said.

The deadline to pass the National Defense Authorization Act is fast approaching, with spending to expire on Dec. 16.

Both congressional chambers passed separate versions of the act this year, The Hill reports, with a final package expected to be unveiled earlier next week.