Washington (CNN) Senate Republicans tried to troll their Democratic colleagues into revealing an intra-party rift and casting potentially politically damaging votes for single-payer health insurance on Thursday.

Democrats didn't take the bait.

In a purely political move, Montana Republican Sen. Steve Daines offered an amendment to the GOP's Obamacare repeal bill Thursday that mirrored, word-for-word, the single-payer insurance program that Rep. John Conyers, D-Michigan, has proposed.

Instead, Democrats -- led by Vermont Sen. Bernie Sanders, who plans to soon introduce his own single-payer "Medicare-for-all" plan, which is expected to draw Democratic co-sponsors -- decried the GOP's handling of the process of overhauling the nation's health care system and largely voted "present."

The idea, however, does have support among leading Democrats, including Massachusetts Sen. Elizabeth Warren and Gillibrand, both potential 2020 presidential candidates.

A handful of red-state Democrats -- North Dakota Sen. Heidi Heitkamp, West Virginia Sen. Joe Manchin, Indiana Sen. Joe Donnelly and Montana Sen. Jon Tester -- as well as Maine independent Sen. Angus King, voted "no." No one voted in favor of the measure, which failed on a 0-to-57 vote with 43 votes of "present."

"I suspect that what Sen. Daines is doing is nothing more than an old political trick, trying to embarrass Democrats," Sanders said on the Senate floor before the vote.

"I suspect it's just a political game," he said. "But I do hope, by the way, at some point within this debate, if we can -- if not, certainly in the near future -- to in fact be introducing a Medicare-for-all, single-payer program. It will be somewhat different than my friend John Conyers' bill in the House, but what it will do is say that in America, if you are rich or if you are poor, if you are a man, woman, and child, yes, you are entitled to health care as a human right and not a privilege."

Missouri Sen. Claire McCaskill called Daines' amendment a "trick." Gillibrand said it was a "sham amendment."

Conyers also urged Democrats to vote against his own proposal.

"The process by which the Senate is considering changes to our nation's health care plan is a sham, and Senate Democrats are right not to take part in it," he said in a statement.

Conyers first introduced his single-payer "Medicare for all" bill in 2003. This year, it has 115 House Democratic co-sponsors. It would eliminate the need for private health insurance companies and premiums in favor of a payroll tax that would lead to all Americans' medical care being covered through the government-run Medicare program. The Urban Institute estimated the tax increases at $32 trillion over 10 years -- though taxpayers would also no longer pay insurance premiums.

Senate Majority Leader Mitch McConnell, R-Kentucky, bashed "single-payer" insurance on the Senate floor ahead of the vote on Daines' amendment Thursday.

"Another idea, from many other Democrats, is to quadruple down on Obamacare with a government-run 'single payer' system. It's called 'single payer' because there is one payer, or insurer, the government," McConnell said.