The 25 to 14 vote in the Kansas Senate on Tuesday comes a week after the state House passed Medicaid expansion, which would allow nearly all poor adults to receive health-care coverage under that joint state-federal program.
But lawmakers don't have enough votes as of now to overcome an expected veto of the measure from Gov. Sam Brownback, a Republican.
"To expand Obamacare when the program is in a death spiral is not responsible policy," Melika Willoughby, Brownback's spokeswoman has said.
However, the Kansas legislature's move is striking, and just the latest in a series of steps by states to expand or change their Medicaid programs on the heels of a failed effort by GOP leaders in the U.S. House of Representatives last week to repeal and replace key parts of Obamacare.
In Maine, where Republican Gov. Paul LePage has vetoed Medicaid expansion efforts by the state legislature, voters are set to cast ballots next fall on a referendum that would authorize expansion.
On Monday, Virginia's Democratic Governor Terry McAuliffe proposed amending language in the state budget to authorize him to move toward Medicaid expansion, which has been opposed by the Republican-led General Assembly.
Also Monday, Georgia's Republican Governor Nathan Deal said he is looking into making changes to the state's Medicaid program "as long as mandates under the basic Obamacare legislation remain in place."
Obamacare requires most Americans to have some form of health coverage or pay a fine. But the law only provides subsidies to help buy private health plans to people who earn 100 percent to 400 percent of the federal poverty.
People who earned below 138 percent of poverty were originally supposed to be made eligible for Medicaid under Obamacare, with the federal government picking up the bill for nearly all the costs of insurance the newly eligible.
But a Supreme Court decision made expansion optional for the states. As a result, in non-expansion states there are millions of people who earn too little to get Obamacare subsidies for private plans, but either earn too much for their state's Medicaid program or are not eligible because they don't have dependent children.
When Trump took office in January, 19 states had still refused to expand Medicaid.
Diane Rowland, executive vice president of the Kaiser Family Foundation, a health-care research group, noted that a number of strongly Republican states had, under President Barack Obama, adopted expansion after initially refusing to consider it.
And Rowland pointed out there has long been pressure within current non-expansion states to expand benefits from the health-care community, including hospitals that desire the revenue that would come from treating more people with insurance.
Hospitals in non-expansion states as a rule have higher levels of "bad debt," which is the cost of treating people who can't pay all or much of their bills because they lack insurance.
Rowland said the departure of President Barack Obama from office earlier this year could remove an inhibition that some legislators had in non-expansion states to approving expansion because it would have been seen as a victory for Obama.
She said that another reason that more states could move toward expansion is a realization by those states that "we would be better to a have expansion money locked in than being on the outside" in the event a Obamacare replacement bill is passed.
While such a bill might, as the failed bill last week would have done, scale back overall federal spending on Medicaid over time, a state that expands before such a bill becomes law would start off with a higher level of current federal funding than non-expansion states, Rowland said.
"Look at Louisiana," Rowland said, referring to Gov. John Bel Edwards' expansion earlier this year, which has led to Medicaid coverage for more than 400,000 Cajun State residents. "It was one of the ways he filled a budget hole."
Rowland said the Trump administration has indicated to states that it is "going to be much more willing to give them waivers" for their Medicaid programs than the Obama administration had been.
Those waivers could include allowing states to impose work requirements on Medicaid recipients, or requiring recipients to pay premiums and some out-of-pocket health costs for their coverage.
Obtaining such waivers, Rowland said, could make Medicaid expansion more palatable to conservative lawmakers.
"Straight expansion is usually a lot easier" for states to implement and administer, Rowland said.
"Putting all these hoops" for Medicaid beneficiaries to jump through, she said, is "for the politics as much as it is for the utility of the program."
Watch: HHS Sec. Price says Medicaid doesn't work