A vote to advance Senate Republican leadership's plan to repeal and replace Obamacare failed late Tuesday -- the latest setback in their party's effort to dismantle the 2010 health care law.

After 9:30 p.m. ET, the Senate rejected a motion 43-57 to waive the Budget Act and advance the proposal, known as the Better Care Reconciliation Act (BCRA).

This contained a proposal from Sen. Ted Cruz, R-Texas, that would allow insurers to sell less expensive bare-bones plans alongside plans that comply with stricter Obamacare standards. And a proposal was added from Sen. Rob Portman, R-Ohio, that would "assist low-income people moving off of Medicaid and onto private insurance plans," according to an aide to McConnell.

Because the Congressional Budget Office (CBO) didn't score the Cruz and Portman proposals, the entire proposal was subject to a 60-vote point of order instead of 51 votes.

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Senator Todd Young, R-Indiana, read the vote results saying, "On this vote the yeas are 43, the nays are 57 ... the motion is not agreed to."

Nine Republican defectors voted against the amendment: Sen. Susan Collins (R-Maine); Sen. Bob Corker (R-Tennessee); Sen. Tom Cotton (R-Arkansas); Sen. Lindsey Graham (R-South Carolina); Sen. Dean Heller (R-Nevada); Sen. Mike Lee (R-Utah); Sen. Jerry Moran (R-Kansas); Sen. Lisa Murkowski (R-Alaska); and Sen. Rand Paul (R-Kentucky).

The Senate adjourned for the evening and will return Wednesday morning at 9:30 a.m. to resume debate and consideration of amendments to the health care bill. The next series of votes are expected at 11:30 a.m. Wednesday.

The Senate's next vote is expected to be on a bill resembling 2015 legislation passed by the upper chamber that would repeal Obamacare, but delay it from taking effect for two years so Republicans can find a replacement plan in that time-frame, which is why it's sometimes called "repeal and delay." Three Senate Republicans came out against this idea last week: Susan Collins, Shelley Moore Capito and Lisa Murkowski. This plan could become even more complicated if Democrats retake control of any part of Congress in 2019. CBO projects that 32 million more people would be left without health insurance in 2026.

Senate Republicans said Tuesday they might also vote on a "skinny repeal" that would be a much more narrow proposal. The Senate is expected to begin what's called a "vote-a-rama" in which senators offer a slew of amendments to the House-passed bill that the Senate opened debate on Tuesday afternoon.