(CNN) Republicans are finding that staying united with President-elect Donald Trump is much easier said than done.

As soon as Trump was declared the winner, top congressional leaders began putting the wheels in motion to do all the things they have campaigned on for years -- overhauling the tax code, repealing and replacing Obamacare, rolling back federal regulations and more.

But just as he did as a candidate, Trump's string of tweets is setting out policies that fly in the face of Republican orthodoxy. Now that he's the elected leader of the party, his proposals are exposing the significant split that already existed between the deal maker reality star president and GOP members committed to a free market driven economy.

No Republican on Capitol Hill wants to publicly oppose Trump, who won the Electoral College race with a huge margin last month and whose poll numbers remain high. The same voters who desperately wanted change in Washington are expecting the GOP-led Congress, which is largely the same, to carry out Trump's agenda. Many don't care about conservative principles. They want results.

Instead of acknowledging the elephant in the room -- they fundamentally disagree on some of Trump's ideas -- Republicans in Congress are trying to pivot the discussion back to where they agree.

In a private 90-minute meeting with Senate Republicans and Mike Pence, the two sides tried to downplay any disagreements. Pence told Republicans their views on free trade are largely in line with Trump's, who has called for fairer deals, attendees said. He sought to allay concerns that repealing the Affordable Care Act, President Barack Obama's signature health care law, without a replacement plan would be problematic, saying certain actions could be taken administratively until Congress passes new law.

And he said he would be a sounding board to Senate Republicans to ensure the two sides stay on the same page, even giving senators his private cell phone number. After the meeting, top Republicans said, further discussion was warranted to ensure the two sides don't splinter.

"Some of the issues out there our members would like to discuss further," said Sen. John Thune, the No. 3 Senate Republican.

How they resolve these ideological differences will be a continual challenge. GOP leaders have already pledged to kick off the new Congress with the health care debate and move quickly to reorder the entire tax system soon after in 2017.

Trade/Tax reform

Trump vowed via Twitter to impose a 35% tariff on any US company that sends jobs overseas that wants to sell goods in America. But for years Republican members of Congress stressed economic plans to change the tax code to provide incentives -- not a cudgel -- to retain businesses from relocating operations.

"Tax reform is the answer to that problem," House Speaker Paul Ryan told reporters Tuesday, when pressed whether he supports Trump's tariff approach.

Oklahoma GOP Rep. Tom Cole, who has foreign companies hiring people at tire plants in his district, batted down the idea of a tariff as an effective tool on CNN.

"I'm not very interested in going to a trade war with countries which are actually have companies that are investing here and employing American workers -- literally by the thousands."

Cole, who stressed the longtime Republican proposal of lowering corporate taxes to create a better business environment, said about Trump's approach, "It's pretty hard to respond to a tweet without knowing the specifics of a proposal."

In some cases Trump would need Congress to enact legislation imposing tariffs, but House Majority Leader Kevin McCarthy split with the leader of his party, saying Monday, "I believe there is a better way of solving a problem than getting into a trade war."

"In general most of our members would be against tariffs and would not support that," North Carolina Republican Rep. Mark Meadows, the chair of the conservative House Freedom Caucus, said Tuesday on CNN. But he tried to shift the focus to other things the GOP Congress wants to work with the new president on in early 2017.

A popular refrain from free market Republicans in Congress is that the government shouldn't be picking winners and losers. But recently Trump upended that notion when he teamed up Pence, who is the governor of Indiana, to package tax breaks to keep Carrier, a manufacturer with operations in the state, from moving hundreds of jobs to Mexico.

McCarthy, pressed on whether the episode amounted to federal intervention, struggled to reconcile how the Carrier deal represented market forces determining the outcome and instead said it is suitable for states to intervene the way that Indiana did.

Michigan GOP Rep. Justin Amash, who has been openly critical about Trump's role on the Carrier deal, told CNN that he viewed a tariff as a '"tax on Americans," and added, "I think he's putting that out there because he knows it won't pass."

Obamacare

Repealing Obamacare is the top priority that has unanimous support within Republican ranks in Congress. Senate Majority Leader Mitch McConnell announced Tuesday legislation to start the process of dismantling the law will be the first item the new Congress takes up in 2017.

"Will there be challenges? Absolutely, yes," McConnell said. "This has been a very, very controversial law. We have an obligation to the American people to change it and to do a better job. If we get Democratic cooperation in doing that, that would be great."

Sen. Chuck Schumer, the incoming minority leader, said the GOP is like "the dog that caught the bus," warning that Democrats would do battle with Republicans on the issue.

"To our Republican friends across the aisle: 'Bring it on,'" the Democratic New Yorker said Tuesday.

Trump has stressed he wants to wipe the health care law away quickly and immediately have a new system in place - a notion he laid out in his first television interview on "60 Minutes" as something that could happen "simultaneously."

But that timeline is running into the realities of the congressional process, something that moves slowly. A repeal of large chunks of the law can occur as early as January because the GOP plans to use a fast-track budget process that cannot be filibustered under the rules of the Senate. But replacing it will take a lot longer -- just how long is a subject of sharp debate in the Capitol.

"They want do reconciliation first and deal with replacement down the road," said Sen. Bob Corker, a Tennessee Republican, who acknowledged lawmakers haven gotten mixed signals from Trump about how to proceed. "A lot of people are saying, 'Hey, we know the issues. Why don't we go ahead and replace it right now?'"

Conservatives want to move quickly.

"I think that health care would be better and cost less when Obamacare is gone, so why would we want to talk three years to get rid of it," said Ohio Rep. Jim Jordan, a top member of the conservative House Freedom Caucus.

Rep. Mark Walker, the incoming head of the Republican Study Committee, a large group of fiscal conservatives told CNN that the framework for dismantling the law in the first hundred days lining up the new system will take some time. "Small businesses are begging us to move quickly but we also want to make sure we're not ripping the rug out from a mass group of people as well."

Republican leaders are plotting out the mechanics of rolling back the law and Ryan stressed in an interview with the Milwaukee Sentinel that repeal and replace wont' happen back to back

"Clearly there will be a transition and a bridge so that no one is left out in the cold, so that no one is worse off," Ryan said.