Some Senate Republicans say they are not abandoning Obamacare repeal, although any progress is likely months away.

Since the Senate failed last week to pass a "skinny" repeal bill, Senate GOP leadership has sent a clear message it is moving on to tax reform and bipartisan talks for a short-term Obamacare market stabilization bill. But some Republicans are not giving up on the years-long promise of repeal despite questions over whether the GOP conference can reach a consensus.

"Unless there is some breakthrough on healthcare reform that gets us 50 votes in the Senate, then the plan is to go into tax reform," Sen. John Thune, R-S.D., a member of Senate leadership, said Wednesday. "If we had a breakthrough on healthcare reform, I think everybody is ready to turn to it and get it done."

Several senators said that they aren't abandoning their repeal efforts, but they need to start work on tax reform.

"We've gotta start forming up consensus around tax reform," said Sen. Thom Tillis, R-N.C. "That takes time. [Senate Majority Leader Mitch McConnell] has to get that track moving."

Sen. Rand Paul, R-Ky., said the chamber is at an "impasse" now.

"We should continue on the tax front, but we should continue negotiating on the health front," he said.

Sen. Ted Cruz, R-Texas, was bullish that the Senate was close to a repeal deal.

"The media celebration that the vote last week came one vote short, I believe, was premature," Cruz said. "We are close, and we could get to yes, and I believe we will."

The statements come a few days after President Trump urged the Senate to continue working on Obamacare repeal after the narrow defeat. Trump tweeted that the Senate would be "total quitters" if it moved away from repeal and even noted that lawmakers should pay what the public pays for Obamacare.

But Senate leadership ignored the threats as it made opening salvos to start work on tax reform. The Senate could leave as early as this week and not return until September, when they face looming deadlines to lift the debt ceiling and fund the government.

In the meantime, work is continuing on a healthcare proposal from Sens. Bill Cassidy, R-La., Lindsey Graham, R-S.C., and Dean Heller, R-Nev.

The proposal would give states block grants for their Medicaid expansions and tax credit money to let them craft their own programs.

It was intended at first to be an amendment to the Senate's Better Care Reconciliation Act, a repeal-and-replace bill that failed last week. The Senate also failed to pass a bill that repealed Obamacare but left it in place for two years while Congress crafted a replacement.

After the Senate defeated the "skinny" repeal bill on Friday, which was meant to be a vehicle to start talks with the House, Graham met with Trump on his block grant proposal.

However, Cassidy said Wednesday that the proposal hasn't been sent to the Congressional Budget Office to be scored to determine the impact on insurance coverage or the federal deficit. Cassidy said he hopes to send it possibly next week, but he is still in talks with governors and state Medicaid directors to determine the formula for providing the funding.

The CBO has not scored an amendment from Sen. Rob Portman, R-Ohio, to add $100 billion in Medicaid funding to entice centrists. Cruz is also awaiting a score for his amendment that would let insurers sell plans that don't comply with Obamacare's regulations, including protections for people with pre-existing illnesses, as long as they sold one plan that does.

"As soon as we get some feedback and CBO scores on [Cassidy-Graham-Heller] and Cruz and Portman, et al., we can have better information to make decisions," Thune said.

But when they would be able to bring up repeal again is unknown. When asked if he would bring up repeal again in September or October, Thune replied that it was "hard to say."

Tillis said Congress has a practical deadline in trying to repeal Obamacare in that the reconciliation budget instructions expire at the end of September.

Republicans have tried to use the reconciliation process to get a bill through the Senate with only 51 votes. The downside is that the bill must meet certain rules, such as reducing the deficit and focusing only on budget and spending levels.

In January, the Senate passed a budget resolution that outlined the instructions for using reconciliation. Those instructions are set to expire in September.

"If we are going to produce a result in reconciliation, then that has to occur before the end of the fiscal year [in September]," Tillis said. "The tax reform discussion will go up on into October and later on in the year."

Tillis added that Republicans would have to do some "dual tracking" to continue the focus on healthcare.

The Senate will have a busy September as lawmakers have to reach a deal to fund the government and raise the debt ceiling. The Senate is also working on a bipartisan deal to stabilize Obamacare's exchanges, which committee leaders want done by the end of September, the end of the federal fiscal year.