Senate Republicans are getting closer to introducing their planto replace Obamacare, Majority Leader Mitch McConnell said Tuesday,though he gave no details and some members said they’re notexpecting action on a bill anytime soon.

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"We’re getting closer to having a proposal that we’ll bebringing up in the near future," McConnell of Kentucky toldreporters after a closed-door Senate GOP luncheon. "We’ve had sevenyears to talk about health care," he said. "We believe we can dobetter than the status quo."

Another key Republican also expressed optimism. “I’m veryencouraged," said Republican Senator Bill Cassidy of Louisiana, whois seen as a pivotal vote. "Of course, it’s not everything I want,but that’s life.”

But Senate Finance Committee Chairman Orrin Hatch of Utah saidthat while Republicans are talking with the nonpartisanCongressional Budget Office on various ideas, "we are not thereyet." Asked when a Senate bill may be introduced, he said, "I doubtit will be real soon."

Campaign pledge

Senate Republicans are seeking consensus on a more modest heathplan than the one passed May 4 by the House as they seek to keeptheir campaign pledge to repeal and replace the 2010 AffordableCare Act. A 13-member working group of Senate Republicans includeslawmakers with varying views.

Senators had said earlier they were weighing a two-step processthat would postpone a repeal until 2020, with an initial priorityon stabilizing premium costs in Obamacare’s insurance-purchasingexchanges in 2018 and 2019 and continuing subsidies that helplow-income Americans afford individual policies.

President Donald Trump told reporters Tuesday, "I’m sure theSenate will follow through and get a bill across the finish linethis summer that will be great health care for Americans." ButSenate GOP members weren’t talking about timetables.

Republicans, including John Thune of South Dakota and SusanCollins of Maine, say stabilizing the markets is vital afterinsurers dropped out of providing individual insurance coverage inIowa, Missouri, Tennessee and other states.

"I hope it could ride together" with long-term changes tohealth-care system, but Congress may need to make short-termrevisions quickly to reassure the markets, Thune said.

Blue Cross

Anthem Blue Cross and Blue Shield said Tuesday that it’sdropping individual exchange coverage in Ohio next year, citing a"lack of certainty of funding" for cost-sharing subsidies thegovernment pays insurers to help reduce low-income Americans’health costs and "an increasing lack of overall predictability" inthe market.

Related: Cuomo takes steps to keep New York insurers inObamacare

Senator John Barrasso of Wyoming, a member of theRepublican leadership team, said senators are discussing a rollbackof Obamacare’s expansion of the Medicaid program for low-incomeAmericans, but not as abruptly as the House bill, H.R. 1628.

The House measure would end the expansion in 2020 as part ofprogram cuts of $834 billion over a decade. He said the Senate GOPis looking at a "glide path" lasting beyond 2020.

Senator David Perdue of Georgia, a Trump ally, said he has a"much better" sense of where the Senate is headed on healthcare.

"I’m still nervous because it’s tough to get 50 votes in thisenvironment," he said. But he added, "I’m seeing more and moreclarity, and a narrower and narrower focus, and a smaller andsmaller difference in the caucus."

Expressing doubts

A number of Senate Republicans have expressed doubt in the lastweek about whether the Senate can pass health-care legislation thisyear, including Lindsey Graham of South Carolina, Richard Burr ofNorth Carolina, Ben Sasse of Nebraska, Jeff Flake of Arizona andRon Johnson of Wisconsin.

The House barely managed to pass its version of the bill with arazor-thin 217-213 vote after weeks of talks with Republicandissidents. The CBO said May 25 that Republicans’ revised billwould undermine insurance markets in some states and result in 23million more people without insurance.

Also Tuesday, the Senate Budget Committee reported that theHouse measure meets requirements to allow the Senate GOP to avoid aDemocratic filibuster and pass a health bill with a simplemajority.

Related: When (or if) ACA repeal vote will take place is upin the air

Democrats had argued that some provisions violated therequirements and that the House would have to vote on the billagain to remove them. The Senate proposal still will have to gothrough a procedure to excise provisions seen as extraneous tobudget issues.

Senate Democrats are ramping up the pressure, calling the Housebill a large tax cut for the wealthy in a thin disguise. The Housebill includes $664 billion in tax cuts over a decade, while alsocutting Medicaid and making other reductions in insurance subsidiesfor low-income and sick people.

Senate Minority Leader Chuck Schumer, a New York Democrat, saidthat Republicans are finding themselves in "no man’s land" bytrying to use a streamlined process to pass an Obamacarereplacement without Democratic support.

‘Political tool’"

The Trump administration’s decision to hold cost-sharingpayments "hostage as a political tool" is to blame for insurancecompanies deciding not to offer coverage in certain areas, Schumersaid.

Senator Ron Wyden of Oregon, the top Democrat on the SenateFinance Committee, on Tuesday called the House bill “Robin Hood inreverse” and said it “moves America back to yesteryear, when healthcare was for the healthy and the wealthy."

Wyden said he has little reason to think Senate Republicans willabandon the House bill’s general framework.

Polls have found the House bill is unpopular. Fifty-five percentof adult Americans have an unfavorable view of the measure, while31 percent view it positively, according to a May 16-22 poll by theKaiser Family Foundation. Only 8 percent of those surveyed thinkthe Senate should pass the House measure without changes.

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