Washington (CNN) That didn't take long. The Republican Party's freshly unveiled bill to repeal Obamacare is already in trouble.

House Republican leaders are proud of their plan to roll back key pillars of the Affordable Care Act. But Tuesday, the proposal has invited criticism from rank-and-file lawmakers, powerful conservative groups and key senators that could threaten the bill's survival.

The fiercest opposition is coming from some of the most conservative Republicans in Congress who have labeled the new legislation "Obamacare Lite" and "Obamacare 2.0." They are warning party leaders that the bill simply doesn't go far enough in gutting the current health care system.

"The bill's dead. Too many conservative groups are coming out against it. There's no way they'll have the votes to pass it in its current form," a conservative House aide told CNN, in a sign of some lawmakers' desire to flex their muscles and make a hard push for changes to the bill.

GOP Rep. Mark Sanford, whose Obamacare bill written with Sen. Rand Paul has been endorsed by the Freedom Caucus, told CNN on Tuesday that he would "lean no" on the House GOP legislation unless changes are made.

"From a conservative's perspective, there are a number of things that need further refinement," Sanford said. "This notion of a refundable tax credit is a big deal, Medicaid expansion is a big deal, the Cadillac tax is a big deal."

Paul told CNN that the current bill would be "dead on arrival" in the House: "I don't think it's ever going to arrive in the Senate. I think it's dead on arrival in the House," the Kentucky Republican told CNN.

JUST WATCHED Conservatives slam House GOP health care bill Replay More Videos ... MUST WATCH Conservatives slam House GOP health care bill 04:05

Rep. Jim Jordan, a member of the House Freedom Caucus, announced that he and Paul would introduce in each chamber a "clean repeal" bill in order to separate out repeal and replace.

Jordan criticized the GOP leadership's health care bill as "Obamacare in a different form."

"That is not what we promised the American people that we're going to do," he said.

House leaders insist that they have the votes they need.

GOP chief deputy whip Patrick McHenry told CNN's Wolf Blitzer that the bill will be passed "almost as it has been introduced with some minor changes," though he admitted, "it won't be without drama."

To try to shore up support, Vice President Mike Pence was on Capitol Hill Tuesday meeting with lawmakers, including conservative members with serious concerns. But members signaled that they want to exercise their political leverage.

"This is the beginning of the negotiation," Paul said. "The House Freedom Caucus' power and the power of several conservatives in the Senate is to withhold our support and to make it better. If they have 218 votes, we won't get any change."

It's not clear how many House Republicans would ultimately vote "no" on the current version of the bill.

The conservative backlash also does not reflect reservations among more moderate members of the party. Health care experts widely agree that the GOP plan would result in millions losing coverage -- an outcome that some Republicans are reticent to try to defend to their constituents back home.

The legislation unveiled Monday would scrap the individual mandate, replacing it with refundable tax credits for individuals to purchase health insurance. It would also restructure Medicaid and defund Planned Parenthood. It seeks to maintain Obamacare's protections for people with pre-existing conditions, but would allow insurers to charge higher premiums to individuals whose coverage has lapsed.

Alaska GOP Sen. Lisa Murkowski has expressed frustration of the effort to tie Planned Parenthood to the health care measure.

"I don't think that the Planned Parenthood defund should be in the ACA bill that we're dealing with. Just don't think so," she said Tuesday.

Crafted through a budget reconciliation process, the GOP Obamacare bill requires a simple majority to pass in the House and Senate. Assuming that no Democrat in the House supports the legislation, House Speaker Paul Ryan can afford to lose around 20 members of his own party.

Senate a major roadblock

In the Senate, where Republicans have a razor-thin margin, just a handful of GOP senators could derail the bill.

Doug Heye, a senior aide to former House Majority Leader Eric Cantor who was involved in the GOP's extended and failed efforts in 2014 to craft an Obamacare replacement bill, said the suggestion that the new GOP Obamacare bill could be dead on arrival -- was hardly a stretch.

"This kind of goes back to everything Republicans have tried and failed to do for the past four years. What is the incentive to vote yes; what is the punishment for voting no? How do you then get to 218?" said Heye, a CNN contributor. "When Boehner said the week before last, Republicans never agreed on health care his entire career, he was right."

Heye was referring to former House Speaker John Boehner's recent prediction that Republicans would not go through with repealing and replacing Obamacare, but rather, "fix" the law, instead.

"In the 25 years that I served in the United States Congress, Republicans never, ever one time agreed on what a health care proposal should look like," Boehner said. "Not once."

Pressure is mounting fast with a slew of conservative groups coming out against the Obamacare bill.

The Club for Growth panned the legislation as a "warmed-over substitute for government-run health care." Heritage Action said there is "no significant difference between the Affordable Care Act" and what House GOP leaders have proposed. "That is bad politics and, more importantly, bad policy," the group's CEO, Michael Needham, said.

JUST WATCHED Republicans divided over Obamacare replacement Replay More Videos ... MUST WATCH Republicans divided over Obamacare replacement 02:14

Freedom Partners and Americans for Prosperity are also opposed to the bill.

The writers of the GOP health care blueprint dismissed the suggestion that it was a modified version of Obamacare.

"This is 'Obamacare gone.' This is the first and most important step to giving relief to Americans from this terrible law," said House Ways and Means Committee Chairman Kevin Brady. "We can act now or we can keep fiddling around and squander this opportunity to repeal Obamacare."

At the White House, Health and Human Services Secretary Tom Price called the House bill a "work in progress," rather than a final bill backed fully by the President.

"This is a work in progress and we'll work with the House," Price said.

And Trump himself tweeted that negotiations are possible.

"Our wonderful new Healthcare Bill is now out for review and negotiation. ObamaCare is a complete and total disaster - is imploding fast!" he tweeted

But after meeting with House Republicans at the White House, Rep. Steve Scalise, the majority whip, said the President "committed in our meeting that he is all-in to making sure that this bill gets to his desk."

This story has been updated.