It will include trying to force votes aimed at drawing attention to the lack of transparency, such as committee hearings, on the GOP legislation. "I think it's much better to have committee consideration of bills, public hearings and to have a full debate".
"This massive piece of legislation that seeks to restructure one-sixth of our economy is being written behind closed doors, without input from anyone", McConnell said, "in an effort to jam it past not only the Senate but the American people".
Several other GOP senators have also expressed their concerns about the secretive process, even though they could call for open committee hearings on the bill. The New York Times reports that there will be no more than 20 hours to debate the bill, and Democrats will have no more than 10 hours to review it. "[We need] people all over this country to put pressure of ever level of government to say in America, you know, we are the wealthiest country in the history of the world". Restrictions on abortion funding in the House bill are opposed by at least two Senate Republicans - Collins and Murkowski - but if removed could thwart House approval of a final measure.
Many Senators drew harsh comparisons to the process of passing the Affordable Care Act eight years earlier, noting that almost 50 bipartisan hearings had been held to workshop that bill, which ultimately included 150 Republican-proposed amendments.
Democrats object to closed-door meetings that Republicans have held in recent weeks to craft legislation to replace Obamacare, formally known as the Affordable Care Act.
O'Halleran said the health care bill process should be similar to another issue looming over Washington, D.C.: tax reform.
Senate Republican leaders would like a vote on healthcare legislation in July, before the July 4 recess if possible. They forced the chamber's top Republican to swat aside reasonable sounding requests, like holding committee hearings.
But the sharp disagreements over the details - including how to reduce the cost of Medicaid and change the rules for health plans on the independent market to lower costs - have produced a complicated and messy drafting process. And Sen. Rand Paul, R-Ky., said it would be "a non-starter" if the developing bill's subsidies are as large as Obama's.
"This radical departure from normal procedure on a bill of such effect leaves the Senate minority little choice but to depart from normal procedure as well", Schumer said.
West Virginia's Republican Sen.
Asked whether leadership has offered any guidance on when the health care vote would take place, three separate aides said in emails to CNN: "No", "Nothing yet", and "Nothing definitive".
The GOP-run House narrowly approved its version of the legislation last month.
"I think the plan, as I said earlier, is to reach the bill on Thursday", Corker said. Creator of Netflix series House of Cards Beau Willimon threw his support behind the Democrats, retweeting MSNBC's Christopher Haynes, who noted there has been no public debate on the Republicans' bill.