Washington (CNN) House Republicans have campaigned on repealing and replacing Obamacare since 2010, but leaders are still working behind the scenes to lock down votes ahead of a Friday vote on the resolution that starts rolling back the law.

Warning that the Affordable Care Act was in a "death spiral," House Speaker Paul Ryan said at a news conference Thursday that Republicans have a responsibility to repeal and replace Obamacare as quickly as possible. "We've got to intervene to prevent this from getting worse," Ryan said.

Following Donald Trump's comments this week that the party must repeal and replace "simultaneously," Ryan insisted that GOP leaders and the President-elect are "in complete sync."

However, Ryan would not offer a firm timeline on when a final repeal bill would land on Trump's desk. "We're not holding hard deadlines only because we want to get it right."

Ryan is facing concerns about the first step of repeal from members who represent the ideological spectrum of the Republican conference.

A significant chunk of conservatives in the House Freedom Caucus -- as many as 20 members -- are leaning against the measure. Some of those want assurances from the leadership that the process to replace the law will occur quickly alongside the votes to repeal it.

Other conservatives are disappointed that the budget resolution doesn't include the broader spending cuts they want to demonstrate their commitment to shrinking government.

Members of the more moderate "Tuesday group" have expressed concerns about backing a repeal effort without more details in place on GOP plans to replace Obamacare and a sufficient transition period so that there aren't disruptions.

House GOP leadership aides continue to express confidence that they have broad support for the measure.

"We're looking forward to a good vote on Friday," Chris Bond, spokesman for House Majority Whip Steve Scalise told CNN, saying that leaders continue to have conversations with members, and there is no talk of delaying the vote.

Ryan also stressed Friday's House vote on the budget resolution is a "procedural vote" to start the process of repealing Obamacare.

"We're going to do this the way Congress is supposed to work, but we do need to move quickly," Ryan said, adding that the Trump administration will be able to provide "regulatory relief" in the meantime as well.

The Senate passed the so-called "repeal resolution" 51-48 in an overnight vote.

Senate Majority Leader Mitch McConnell Thursday detailed the path forward.

"The next step will then be the legislation to finally repeal Obamacare and move us toward smarter health policies. The repeal legislation will include a stable transition period as we work toward patient-centered health care," McConnell said on the Senate floor Thursday.

"We plan to take on the replace challenge in manageable pieces with step-by-step reforms," he added. "We can begin to make important progress within that repeal legislation, and we'll continue to work with the incoming administration and the House in developing what comes next."

Proving more difficult to repeal than expected

But the last-minute internal lobbying shows how much more difficult the process of dismantling the law is proving to be, even with Republicans in control of both chambers of Congress and Trump about to be sworn in. House Republicans voted multiple times over the past two years to repeal all or parts of Obamacare, but faced with presenting details for what will come next is causing some to be nervous about the process.

Freedom Caucus Chairman Mark Meadows told reporters on Wednesday he is undecided on how he will vote on the measure, but the group of conservatives is split. Without enough of its members agreeing on a position the caucus will not take an official position.

One factor that is helping House GOP leaders is that two outside conservative advocacy groups -- Heritage Action and the Club For Growth -- are "scoring" the vote, meaning they are using the vote as a way to keep tabs on how members vote on key issues.

Fiscal conservatives in the Republican Study Committee are pressing for their own budget to be added as an amendment ahead of Friday's vote, a move to go on record with their concerns.

"This budget is not the road map to fiscal responsibility House conservatives would have preferred," RSC Chairman Mark Walker told CNN in a written statement. The North Carolina Republican said it was important to move ahead with the resolution to fulfill a pledge to repeal Obamacare but added, "we must immediately act to ensure that the FY 2018 budget balances and brings America's fiscal house in order" saying the push to add his plan was a "marker" to begin that process.

But likely the bigger issue that will propel some wavering members is that Trump has publicly called for repealing and replacing Obamacare to be a top priority for the early days of his administration.

Fate of taxes

Another big question that some conservative House Republicans are pressing Ryan for clarity on, according to a GOP aide, is whether Obamacare taxes -- which include taxes on high-income Americans and insurers and other providers -- would be repealed immediately as a part of the budget reconciliation bill.

Many conservatives who want smaller government and less taxes are advocating for an immediate repeal of the taxes in the Affordable Care Act. But others worry that that money is necessary to fund the GOP's replacement plan.