JEFFERSON CITY, Mo. — Several thousand disabled and elderly Missouri residents will remain without personal care services after lawmakers on Wednesday refused to override a gubernatorial veto but instead pledged to keep working on a way to reverse the budget cuts.

Senate President Pro Tem Ron Richard and House Speaker Todd Richardson said they have asked colleagues to try to develop a plan in the next three weeks to undo the cuts to in-home and nursing care for about 8,300 people.

Their announcement came minutes before an effort by House Democrats to override Republican Gov. Eric Greitens’ veto of one potential solution failed on a largely partisan 49-106 vote.

“It’s our job even in tough budget years to protect our most vulnerable citizens,” Richard said in a statement. “Preserving funding for in-home and nursing care is important to both chambers, and together with the House, we can come up with a plan to keep those funds for senior services intact.”

Richard said the hope is to come up with a plan by Oct. 6 and ask Greitens to call lawmakers back in for another session.

The programs fund part-time caretakers providing services such as bathing and grooming to low-income people enrolled in the Medicaid health care program. The budget that took effect July 1 cut funding, meaning people must have a greater level of disability to be eligible or may qualify for fewer hours of service.

Lawmakers in May passed a bill to restore funding by allowing the state’s administration commissioner to take up to $35.4 million from unspent money in dedicated funds in order to maintain the current level of in-home and nursing services.

But Greitens in June vetoed the bill, which he called “an unconstitutional, one-time, fake fix to a real problem.”

Since then, both Republicans and Democrats have been scrambling for a solution. While House Democrats led a push to override Greitens, Republican Lt. Gov. Mike Parson called on lawmakers to convene a special session to address the problem.

Wednesday’s session focused on gubernatorial vetoes would have been a prime opportunity for another session. But legislative leaders couldn’t pull together a plan that would muster support from the three-fourths of lawmakers needed to call a special session.

Democrats bemoaned the lack of an immediate solution for the cuts, which are being phased in now.

“The daily suffering caused to Missourians will hang on all of our heads,” said Rep. Deb Lavender, a Democrat from suburban St. Louis.

One alternative is to fund the personal care services with money saved by reducing a tax credit for low-income seniors and disabled residents who live in rental housing — an option endorsed by House members during the regular session.

But House Minority Leader Gail McCann Beatty said Wednesday that reducing the so-called “circuit breaker” tax break is “a nonstarter” for House Democrats.