Four Republican senators are calling their bill to overhaul Obamacare as the last chance to repeal the healthcare law even though the legislation leaves parts of the law's regulations and taxes intact.

"If you believe repeal and replace of Obamacare is a good idea, then this is the best approach," said Sen. Lindsey Graham, R-S.C., who is sponsoring the bill with Republican Sens. Bill Cassidy of Louisiana, Dean Heller of Nevada and Ron Johnson of Wisconsin.

"This is our last shot," Johnson added at a press conference Wednesday outlining the legislation.

The bill would provide $1.2 trillion to states in the form of block grants from 2021 to 2026. It would eliminate Obamacare's individual and employer mandates and medical device tax, but leave taxes on insurers and investments.

Graham aimed to use the Wednesday rollout of a new single-payer bill from Sen. Bernie Sanders, I-Vt., to strike a contrast with the Republicans' effort.

He called single payer "Berniecare," and added that it would make the U.S. like Greece, which has had to make severe austerity cuts as part of a massive financial crisis.

"What Bernie is doing is a great disservice to our country," Graham added.

But the Republican bill faces a major time crunch to clear the Senate. Instructions for Republicans to use reconciliation, which lets a bill bypass a filibuster, expire at the end of the month.

The bill also has some resistance from conservatives. Sen. Rand Paul, R-Ky., recently told Politico that it doesn't appear to repeal as much of Obamacare and leaves in too many taxes and regulations.

The bill's co-sponsors say that the legislation may not be perfect but it is the best they have got, especially after other repeal efforts failed in late July in the Senate.

"This is far better than Obamacare," Johnson said.

The senators are planning a mad dash to muster enough support for the bill before the end of the month. Senate Majority Leader Mitch McConnell has told them that he will hold a vote if they can get the 50 needed for it to pass the chamber, with Vice President Mike Pence being able to break any tie.

The quartet may be on their own to muster votes. Cassidy hinted to the Hill newspaper that McConnell isn't going to whip votes for it.

The senators are hoping to get a lift from Republican governors who didn't endorse other repeal efforts.

Graham said about 14 governors are on board, and he is hoping to get to 20.

But the senators hinted at the work that is left to do.

For instance, popular Republican Nevada Gov. Brian Sandoval has not signaled support. Heller, a vulnerable Republican up for re-election next year, said it is a "work in progress."

Sandoval blasted the Senate GOP's initial Obamacare repeal bill called the Better Care Reconciliation Act because of its $770 billion in cuts to Medicaid. Nevada is one of the few red states to wholeheartedly embrace the Medicaid expansion, which has enrollment of more than 200,000 people in the state.

They also hope that the White House can help in luring governors' support

"The idea that we can do this by ourselves is unreasonable," Graham said.

He also prodded GOP leadership.

"Everybody is telling us get us 50 votes and we'll help you," he said. "Here is my challenge to the Republican leadership: Act like this matters because it does. I am not ready to move on. I don't want this bill to die because we are just tired of dealing with healthcare."

Another major question mark is the impact the bill would have on Obamacare's regulations protecting people with pre-existing conditions and mandating coverage of essential health benefits such as maternity care and hospitalization.

The regulations have been a major sticking point in other repeal efforts because Republicans have been reticent to reduce protections for people with pre-existing conditions.

Cassidy told reporters that the money would be provided to states similar to the block grants under the Children's Health Insurance Program. He added the bill includes tools and mechanisms that states can use to expand the risk pools on the individual market in their states. The individual market is for people who don't have insurance through their job and it includes Obamacare's exchanges.

Cassidy did not go into what the mechanisms would be. He did say that there could be additional flexibility granted by Health and Human Services Secretary Tom Price to meet insurer regulations.

"By putting it through the CHIP program, we recognize that the secretary has a great ability to provide waivers," Cassidy said. "No governor has complained that I know of about the CHIP program being too restrictive on what he or she is able to do."

But senators also emphasized they are not lowering patient protections, which have been a key driver in rising insurance premiums.

Former Pennsylvania Sen. Rick Santorum, who has been aiding the effort, told reporters that the legislation guarantees coverage for pre-existing conditions and a regulation to keep insurers from charging those customers more money.

Johnson added that states could adopt high-risk pools or reinsurance programs that help defray the costs of high-risk enrollees.

Graham said that the bill does not lower "guardrails" for patient protections.

"We are trying to get as many approaches to helping sick people as there are out there," he said. "Under Obamacare the innovation is almost zero, under our block grant approach innovation is pretty wide."