The House version of the AHCA prohibited Americans from using federal tax credits to buy health care plans that covered abortion.
The Senate bill does not change current coverage for pre-existing conditions.
The bill would phase out the extra money Obama's law provides to states that have expanded coverage under the federal-state Medicaid program for low-income people.
The protesters are yelling "no cuts to Medicaid" as they are being led away.
As senators struggle to develop a health care bill, their handiwork appears to be too moderate for some Senate conservatives and too conservative for some Senate moderates.
The subsidies are expected to be linked to recipients' income in the Senate bill, a "major improvement" from a measure approved last month by the U.S. House of Representatives that tied them exclusively to age, Republican Senator Susan Collins of ME said.
Senate Republicans on Thursday unveiled their version of a bill to repeal most of Obamacare after weeks of closed-door talks and secret negotiations among a working group of GOP lawmakers.
The budget is up for votes in both the House and Senate today. "But Republicans believe we have a responsibility to act and we are for our constituents, our states, and our country".
"I think it is extremely hard, and it's even more hard if you care about maintaining coverage for millions of Americans who need health insurance coverage", said Collins, who is concerned about Medicaid, opioids and the process by which the bill has been written.
Democratic Senator Patty Murray of Washington said in a statement that leaked details of the bill indicated it was "every bit as devastating for families' bank accounts and healthcare coverage as the disastrous bill that passed in the House".
The Republican bill would provide $50 billion through 2021 as a short-term measure, but a separate pot of money would provide another $62 billion from 2019 through 2026, the draft said. The underlying reasons we are in crisis are that for-profit health insurers and drug maker stakeholders remain in legislative control of health care policy.
Mr. McConnell is determined to get a vote on the bill by the end of next week, before a break for the Fourth of July holiday, but he still does not have enough committed votes to ensure passage.
Trump then acknowledged that his criticism may not be doing Senate Republicans any favors in winning over their Democratic colleagues.
"I'm still hoping we reach impasse and we go back to the idea we started with, which is repeal Obamacare", Paul said.
While the House legislation pegged federal insurance subsidies to age, the Senate bill would link them to income as the Affordable Care Act does.
Democrats say GOP characterizations of Obama's law as failing are wrong and say the Republican plan would boot millions off coverage and leave others facing higher out-of-pocket costs. "Because of this, I can not support it as now drafted, and I do not believe it has the votes to pass the Senate".
The healthcare bill will be released to the Republican Senate Conference on Thursday morning and posted online, senators said.
The Senate bill would also reduce subsidies now provided to help people without workplace coverage get private health insurance, said Caroline Pearson, a senior vice president of the health care consulting firm Avalare Health.
The Senate bill would give states more leeway in opting out of the ACA's insurance regulations through expanding the use of so-called "1332" waivers already embedded within the law.
So what do conservatives get out of this bill?
The Senate plan drops a requirement for individuals to have health insurance and eliminates taxes on the wealthy. Among those signing the letter were top executives of AmeriHealth Caritas, Molina Healthcare, Blue Shield of California and Healthfirst, in NY. "That's what we're told it might be", said Republican Senator Bill Cassidy of Louisiana.
In addition to vowing to deliver on his stalled plan for a new wall on the U.S. -Mexico border - perhaps paid for in part through solar energy generation - the president said he would seek new legislation to place conditions on immigration to the United States. This process will allow senators to draw attention to the causes they have championed and potentially change the final bill.
"My sense of it is there will still be some differences that need to be worked out", said Senator Marco Rubio of Florida.
The Congressional Budget Office is expected to release an analysis of the bill early next week. "It's time that Americans received #BetterCare", he said in a tweet.