WASHINGTON - Senate Republicans unveiled a "discussion draft" of the bill Thursday of their plan to repeal and replace Obamacare that would end the health care law's penalties for people who don't buy insurance, cut back an expansion of Medicaid, but would keep more protections for people with pre-existing conditions, compared to a House-passed bill. 

The measure would also eliminate federal funding for Planned Parenthood and provide tax credits based on income, making more money available to lower-income recipients to help them buy insurance. The House bill tied its tax credits to age.

Senate Majority Mitch McConnell, R-Kentucky, aims to hold a vote on the legislation before lawmakers leave at the end of next week for the week-long July 4 recess.

A cost estimate of the bill from the nonpartisan Congressional Budget Office (CBO) is expected to be released by early next week. White House staff met with Senate Republican staffers Wednesday night on Capitol Hill to review the bill.

Republicans need a simple majority to pass it, rather than a supermajority since they're using the budget reconciliation process. They may still have to rely on Vice President Mike Pence to cast a tie-breaking vote. The Senate currently has 52 Republicans and 48 Democrats. That means if all Democrats vote against the bill, only three no votes from Republicans can torpedo it.

Even if Republicans are successful in getting it through the upper chamber, they would then still need to reconcile it with a version passed by the House in early May, reach a bicameral agreement with House Republicans, and hold votes in the House and Senate on that version again.

The House bill, narrowly passed in a 217-213 vote on May 4, would significantly reduce the funding for Obamacare subsidies, revamp tax credits so that they're tied to a person's age, freeze the Medicaid expansion in 2020 and allow states to seek waivers from a rule that requires states to offer essential benefits in their plans and a provision that prevents insurers from charging people with pre-existing conditions more money compared to healthy people. Instead of Obamacare's insurance mandate, the House Republican bill would incentivize people to have continuous coverage whereby if coverage is interrupted for more than 63 days, insurers can charge a 30 percent penalty over the original premium for one year.

The CBO didn't release its cost estimate on the House bill until May 24, which projected that 23 million more people would be without health insurance over the next decade under the bill.

The Senate's version was supposedly crafted by a working group consisting of 13 Republican men -- and no women -- but one of the group's participants, Sen. Mike Lee, R-Utah, said even he's been left in the dark. Lee said it's "apparently being written by a small handful of staffers for members of the Republican leadership in the Senate."

Other Senate Republicans voiced frustration that the process has been too secretive and out of the public eye. Senate Republicans don't intend to hold any committee hearings on the bill, despite their commitment to so-called "regular order."

Nearly three-quarters of Americans said Senate Republicans should discuss their health care plans publicly, according to a CBS News poll released Tuesday. A quarter of the public, by contrast, said it should be developed in private. It also found 57 percent said Obamacare needs some changes, 28 percent said it should be repealed entirely and 12 percent said it should be kept in place.