Senate Democrats on Thursday defeated a series of Appropriations panel amendments designed to foil the implementation of ObamaCare.
With the congressional budget process at a stalemate, the remarks from Rubio signal what could become another showdown over funding for the Affordable Care Act.
The health appropriations bill that advanced in committee Thursday provides more than $5 billion to the agency charged with overseeing healthcare reform.
Amendments offered by the GOP would have delayed the employer and individual mandates, rescinded funds for the insurance exchanges and the Independent Payment Advisory Board (IPAB), and stopped the exchanges if technical glitches or other problems came up before Oct. 1.
The measures were defeated on mostly party-line votes, with vulnerable Democratic Sen. Mark Pryor (Ark.) supporting the repeal of funds for the IPAB.
The budget for the controversial Medicare cost-cutting board would have been transferred to a program supporting pediatric medical residents.
The author of that amendment, Sen. Jerry Moran (R-Kan.), also moved to spend $1.35 billion of the exchanges' budget on the National Institutes of Health.
Moran's two amendments were defeated 15-15 and 16-14, respectively.
Sens. Dan Coats (R-Ind.) and Thad Cochran (R-Miss.) offered the proposal to stop the exchanges from operating if one fails to accept applicants on Oct. 1.
Sen. Tom Harkin (D-Iowa), who leads the Health Appropriations subcommittee, said the measure would shut down the marketplaces over something as simple as an enrollment website crashing.
"This is another attempt [for Republicans] to do what they can to stop the Affordable Care Act from being implemented," Harkin said.
"We know that the exchanges are going to open" on schedule, he added.
Thursday's markup advances the 2014 Labor, Health and Human Service and Education Appropriations bill. The legislation would spend about $164 billion total.
In a stark contrast to past appropriations bills, which have often garnered bipartisan support, the measure was approved on a party-line vote of 16-14.
On the transportation, agriculture, veterans and energy titles, between six and eight Republicans voted yea with Democrats even though the bills violate budget caps put in place by the sequestration law.
The National Republican Senatorial Committee (NRSC) quickly jumped on the yea vote from Sen. Mark Begich (Alaska), saying the first-term Democrat had endorsed the "ObamaCare train wreck."
"When the cameras are off behind closed doors, Alaskans cannot trust Mark Begich," said NRSC spokeswoman Brook Hougesen in a statement.
The White House also weighed in Thursday, calling GOP arguments against the employer mandate delay disingenuous.
"This is about an attempt to sabotage the Affordable Care Act," said White House spokesman Jay Carney at a press conference.
"They want to kill the bill. They want to kill the law. They want to undermine the law. They've made that clear. They're proud of it, and that's a fine position to take.
"But it's the law. And it's been upheld by the Supreme Court … It's being implemented responsibly," he said.
—This story was updated at 2:05 and 6:00 p.m.