By Ginger Gibson and Richard Cowan

WASHINGTON (Reuters) - It is no surprise that Democrats in the U.S. Congress will oppose Donald Trump but the most important resistance to fulfilling the president-elect's agenda is beginning to emerge from Republicans on Capitol Hill.

A small number of influential Republicans in the Senate are threatening to block appointments to Trump's administration, derail his thaw with Russia and prevent the planned wall on the border with Mexico.

The party held onto control of the Senate at the Nov. 8 election but by only a thin margin, putting powerful swing votes in just a few hands.

That empowers Republican Senate mavericks such as Rand Paul of Kentucky and Ted Cruz of Texas. Both were bitter rivals to Trump in the 2016 Republican presidential primary.

Paul, a libertarian lone wolf, says he will block Senate confirmations if Trump nominates either former New York Mayor Rudy Giuliani or former U.N. Ambassador John Bolton to be secretary of state.

South Carolina's Lindsay Graham has started publicly outlining places he might be willing to oppose Trump. He is against the Mexican border wall and is delivering warnings against Trump's intention to revoke legal status for undocumented immigrants brought here as children - although that would not require congressional approval.

Graham, a traditional Republican foreign policy hawk, strongly disagrees with Trump's attempt to improve ties with Russia.

"I am going to be kind of a hard ass" on Russia, Graham told reporters recently. "We can’t sit on the sidelines" and let cyber attacks blamed on Russia "go unanswered."

The early stirrings of opposition from Senate Republicans are a sign that the New York businessman, who has never held public office, might run into harsh political realities soon after taking office on Jan. 20.

Other Senators who might defy Trump are Arizona's John McCain and Jeff Flake, Nebraska's Ben Sasse, Florida's Marco Rubio, Maine's Susan Collins and Alaska's Lisa Murkowski, said senior Senate aides and lawmakers.

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These lawmakers have ruffled feathers in the past and some have a good political reason not to fear Trump: Paul, McCain, Murkowski and Rubio do not have to run for reelection until 2022. Graham, Collins and Sasse will have to face the voters in 2020; Cruz and Flake have an earlier election, in 2018.

Senate Majority Leader Mitch McConnell, whose job is to keep the Republicans in line, knows the challenges ahead. A senior Republican aide said McConnell is “loathe” to spend time trying to move bills that lack the needed Senate votes.

McConnell is aware he will not have the support of some of his own lawmakers on bills that could pass the Republican-controlled House of Representatives, such as appropriating money to build the Mexican wall and further abortion restrictions, the aide said.

DEMOCRATIC STRAYS

But Trump has a history of taming what appear to be well-entrenched Republican opponents. He won the party nomination against all the odds and some of his staunchest opponents like Rubio and Cruz ended up endorsing him.

And swing votes in the Senate cut two ways. The Democrats have their own potential renegades such as West Virginia's Joe Manchin, who has already declared his support for Trump's nomination of Republican Senator Jeff Sessions as attorney general.

Such swings by Democrats toward Republicans may be likelier ahead of the 2018 elections, when Democrats must defend more vulnerable Senate seats than Republicans. Senate Democratic Leader Chuck Schumer must deal with this. Trump said over the weekend he and Schumer "always had a good relationship."

Republicans are likely to control only 52 seats in the 100-seat Senate, meaning three defections within the party are enough to block cabinet appointments which only require 50 votes. Vice President-elect Mike Pence would break 50-50 ties.

The task for McConnell gets more difficult when it comes to passing legislation, which requires 60 votes, known as cloture, to allow a bill to move forward. If Trump plans to sign a bill while in office, perhaps one that will change immigration law or restrict abortions, McConnell will have to keep all Republicans in line and win over an additional eight Democrats.

Trump could deliver on campaign promises that do not require legislative approval like blocking the Trans-Pacific Partnership trade deal or ending the Iran nuclear pact. The repeal of the Affordable Care Act, also known as Obamacare, enjoys robust Republican support and would be done through a legislative maneuver that does not require any Democratic support.

Collins and Murkowski have a history of crossing the aisle to join Democrats and could shy from abortion restrictions.

Cruz has never feared disrupting Senate business to prove a point or seek concessions in legislation.

Sasse did not waver from his staunch criticism of Trump through the campaign. Flake has said he is “eating crow” after Trump’s win, but he could defect on immigration and border security, issues he has previously joined with Democrats on.

Paul was asked last week on MSNBC if he would put a hold on Giuliani or Bolton. In the Senate, a hold allows a single senator to delay a confirmation. He left open the possibility of such a move, saying, “I feel pretty strongly about it.”

He said: "We have a 52-48 majority, all it would take is two or three Republicans to say they can’t go along with Giuliani and can’t go along with Bolton.”

(Reporting by Ginger Gibson and Richard Cowan; Editing by Kevin Drawbaugh and Alistair Bell)