Ohio lawmakers threatened overrides earlier this month when Republican Gov. John Kasich vetoed a number of bills delivered to his desk -- and on Thursday the lawmakers succeeded in a case that affects gun owners. But they failed to do the same regarding a proposed abortion restriction that some had called one of the most potentially far-reaching in the nation.

The gun bill allows off-duty police officers to carry concealed weapons and strengthens penalties against certain illegal firearm purchases, FOX 8 Cleveland reported.

Kasich opposed language that shifted the burden of proof in self-defense cases from the defendants to the prosecutors. He also took issue with the omission of a “red flag” law that allows authorities to take away firearms from people who demonstrate they are a danger to themselves or others.

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“This idea’s omission from this legislation is a shortcoming that I cannot accept,” Kasich said, according to the Wall Street Journal.

But the state's GOP-led Legislature disagreed. The House voted 67-22 in favor of the override, following a 21-11 Senate vote earlier Thursday.

In a win abortion-rights advocates, Statehouse Republicans came up one vote shy of reversing Kasich's veto of the so-called "heartbeat bill." While the House passed the override measure, the Senate could muster only 19 of the required 20 votes.

The bill would have banned abortions after the first detectable heartbeat of a fetus, which can come as early as six weeks -- or before most women know they are pregnant.

Kasich, who leaves office in January, called the bill unconstitutional and hoped to avoid costly litigation that would have most certainly resulted from its passing.

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Lawmakers also successfully reversed Kasich's veto of a bill that increases benefits for the families of deceased first responders while providing a $13,000 pay increase for themselves.

"I would have signed such a bill into law," Kasich wrote in his veto message, according to the Cincinnati Enquirer. "Unfortunately, I cannot support or condone the last-minute rush to include a controversial pay raise for elected officials into what was an otherwise commendable bill."

Lawmakers, meanwhile, preferred to stress the bill's importance to the families of first responders rather than to their own bank accounts.

“I am delighted that the governor’s Grinch-like veto was resoundingly overridden and that the spouses of the fallen first responders will, after seven years of trying, get the enhanced benefits they deserve," Republican state Rep. Bill Seitz told Cincinnati's FOX 19 Now after the override. "Having virtually every elected official in the state as advocates for the bill really helped push this over the finish line."

“I am delighted that the governor’s Grinch-like veto was resoundingly overridden and that the spouses of the fallen first responders will, after seven years of trying, get the enhanced benefits they deserve."
— Republican state Rep. Bill Seitz

Some have speculated whether Kasich will mount a 2020 presidential bid. In an interview with "Fox News Sunday," he chided the current political climate and said "all options are on the table."

"We look every day -- I have a team of people who look every day at the factors that go into a consideration like that. We assess it, and at some point I will make a decision," he said.

Kasich suspended his 2016 presidential bid in May of that year and only won Ohio.

The Associated Press contributed to this report.