So much for Donald Trump's honeymoon. Whether it's his cabinet picks or his policy goals, the U.S. president's judgment is already bumping up against resistance — and it's coming from within his own Republican Party.

At issue are the signature policy planks and goals that helped vault Trump to the White House: His Mexican border wall, an executive order limiting immigration from Muslim-majority countries, his $1-trillion infrastructure spending plan, and his promise to speed through a repeal of the Affordable Care Act.

The dissent has even put his cabinet picks in peril, despite the Republicans' small majority in the Senate.

What should have been Trump's period of goodwill seems to have eroded amid a frenzy of post-inauguration executive decisions, says Mark Harkins, a congressional analyst with the Government Affairs Institute at Georgetown University.

"Normally, a new president has a honeymoon period," he says. "It's unusual to see this much opposition right after you've been elected."

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Senators John McCain, left, and Lindsey Graham were among Republicans who initially opposed Trump's selection of Rex Tillerson as secretary of state. (Jonathan Ernst/Reuters)

Rarely shy of boasting about his record, Trump has already set a record of another sort with his choice for secretary of state, Rex Tillerson.

On Wednesday, the former ExxonMobil executive squeaked through in the most opposed confirmation process for that post in Senate history. This, despite Republican senators John McCain, Lindsey Graham and Marco Rubio reluctantly backing down from their threats to block Tillerson due to concerns about his cosy ties with Russia.

Tillerson was confirmed in a 56-43 vote, a nail-biter considering how his predecessors sailed through. It was 94-3 in favour of John Kerry, 94-2 for Hillary Clinton, and 85-13 for Condoleezza Rice.

Republicans 'walking a fine line'

It's becoming increasingly clear that while Democrats can slow down his agenda, Republicans can kill it. That dynamic could soon be tested in Congress.

Trump's proposal to build a Mexico border wall is reportedly meeting defiance from conservative lawmakers. More than a dozen congressional Republicans told CNN they would vote to block the appropriation of funds to construct the estimated $14-billion wall.

"The fault lines are there," says Mike Tanner, a senior fellow specializing in domestic policy with the Cato Institute. "The Republicans are walking a fine line right now."

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Trump's actions raised concerns about his diplomatic tact this week when details leaked to reporters about tense phone calls with allied leaders in Australia and Mexico. The tensions will add to the challenges his new secretary of state Rex Tillerson, right, is about to inherit. (Reuters)

How fine a line? Two votes in the Senate cut it pretty darn close.

That margin could end Betsy DeVos's bid for the secretary of education job, after she flubbed her testimony in confirmation hearings. Two Republican senators, Lisa Murkowski of Alaska and Susan Collins of Maine, objected to the president's choice — enough to imperil DeVos's confirmation on Monday.

If it comes to a 50-50 split, Vice-President Mike Pence would be forced to cast the tiebreaker to approve DeVos. Such a scenario has never happened.

The Senate has rejected a president's cabinet nominee only nine times. The last time was in 1989, when George Bush's defence secretary nominee John Tower was defeated 53-47.

"All that drama occurs because two Republicans defected. What happens if two Republicans defect on infrastructure? Or on Obamacare?" Tanner says.

"If the Democrats really want to make a point and defeat somebody, or hobble some particular legislation to make an opposition point or because they actually care, then wow — the Republicans have a problem."

At least 19 Republicans have denounced Trump's executive order closing U.S. borders to people from seven Muslim-majority countries. Several conservative lawmakers have also raised concerns about the speed with which the administration is moving toward repealing the Affordable Care Act.

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Paul Ryan, newly elected Speaker of the U.S. House of Representatives, speaks to the House in October 2015. Congressional Republicans have expressed objections to some of Trump's policies. (Gary Cameron/Reuters)

Cautious Republican lawmakers have also "slowed down" talk of killing the health-care law, worried that lack of a suitable replacement would leave some 20 million Americans uninsured, Tanner says.

"At first, we were talking about how we'll have a [repeal] bill on the president's desk by August; now we're talking maybe May."

It's not uncommon for presidents to face dissent from their own party over time. The extraordinary scenario here is how soon the Republican pushback against Trump is happening.

Another potential obstacle to watch is congressman Rodney Frelinghuysen, a Republican from New Jersey who will chair the House appropriations committee. It's a powerful post in Trump's America, Harkins says, as Frelinghuysen will have a grip on the federal purse strings.

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Betsy DeVos testifies before a Senate committee confirmation hearing to become secretary of education. Her confirmation could be in jeopardy, as two Republican senators have said they will not vote for her. (Yuri Gripas/Reuters)

Trump's proposal to introduce a $1-trillion infrastructure spending bill would fly in the face of Republican orthodoxy.

"Increasing our debt by a trillion dollars? That's where I think the pushback is coming," Harkins says.

Frelinghuysen was one of the few House Republicans to disavow Trump during the campaign, and he has publicly denounced the president's controversial border-closing executive order.

A revision in an omnibus appropriations bill could restrict money from being spent on the executive order, including the salaries of immigration and customs agents. That would prevent them from working.

Trouble in poll numbers

In the lead-up to mid-term elections in 2018, Steve Billet, an expert on legislative affairs at George Washington University, expects congressional Republicans to base their willingness to bend with the White House line on the president's eventual approval ratings. Trump scored a 51 per cent approval rating on Jan. 31 in a conservative-leaning Rasmussen Reports poll, though his numbers inched up on Friday to 56 per cent.

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Activists gather at Portland International Airport in Oregon to protest against Trump's travel ban. (Steve Dipaola/Reuters)

A Quinnipiac University poll released days before he entered office had his favourability at just 37 per cent. If Trump's ratings drop again into the low 30s, Billet foresees trouble.

"There's enough concern in the Republican rank and file about his policies," he says.

"Many of them would simply abandon him if it looks like he's having problems. If you're a Republican member of Congress, you might just think, 'I can't run with this guy.'"

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People pass graffiti along the border structure in Tijuana, Mexico. Trump moved aggressively to tighten immigration controls, signing executive actions to jump-start construction of his promised U.S.-Mexico border wall. (Julie Watson/Associated Press)