One party-control of government does not mean no checks on the White House. Yes, Senate Democrats will be watching President-elect Donald Trump, but so will members of his own party.

In the past week, several Senate Republicans have raised warning flags over Mr. Trump’s nomination for secretary of State, ExxonMobil executive Rex Tillerson. They have also crossed the president-elect by demanding an investigation of Russian election-related hacking, as reported by United States intelligence. Trump says Russia has nothing to do with the hacking.

It’s unusual for lawmakers on the president’s team to actually block him when their party holds both chambers of Congress and the White House. But it’s not unheard of. Republican George W. Bush could not get immigration reform through the House when he tried it. And plenty of Democrats defected on health care under Bill Clinton. Further back, Democrats refused to let Franklin D. Roosevelt pack the Supreme Court.

“One-party government improves the odds of support, but it does not guarantee anything,” notes historian Julian Zelizer, of Princeton University in New Jersey, in an email.

Right now, Republicans are pretty excited about Trump’s early priorities: rolling back regulations, repealing the Affordable Care Act, and reforming the tax code. But they will hold only a narrow 52-to-48 majority in the new Senate – and a dozen GOP senators either refused to endorse Trump or rescinded their endorsement. Sen. Jeff Flake (R) of Arizona famously said he would not be able to attend the GOP convention last summer because he had to mow his lawn.

If Democrats hang together, it would take only three Republicans to deny Trump a majority, not to mention the 60-vote threshold required for most major Senate business.

Even before Trump takes office, several Republicans are already signaling that they will be willing to stand up to Trump on certain issues.

Going maverick

The defense hawk duo, Sens. John McCain (R) of Arizona and Lindsey Graham (R) of South Carolina, are alarmed generally by Trump’s friendly attitude toward Russia, and in particular by the hacking issue and the nomination of Mr. Tillerson.

ExxonMobil has extensive business dealings in Russia, and Tillerson has criticized US sanctions on Russia. He has been honored by the Kremlin with a medal of friendship.

“Anybody who’s a friend of Vladimir Putin must disregard the fact that Vladimir Putin is a murderer, a thug, a KGB agent,” said Senator McCain, speaking of Tillerson, on CNN on Monday.

A Trump critic who revoked his endorsement of the president-elect, McCain easily won reelection in a Trump state – giving him plenty of latitude to say and do as he wants (which he usually does anyway).

Sen. Marco Rubio (R) of Florida has also raised “serious concerns” about the nomination, and is promising a “thorough hearing.” In theory, those three senators alone could be enough to derail the nomination.

Senate majority leader Mitch McConnell (R) of Kentucky has backed Tillerson, but he has pushed back on Trump in his usual succinct way.

On Monday, he said he supported a congressional investigation of Russian hacking. “It defies belief that some Republicans in the Senate are reluctant to either review Russian tactics or ignore them,” Senator McConnell told reporters. “The Russians are not our friends.”

Like McCain, Graham, and many others in the Senate – including Democrats – McConnell is very worried about Russia expanding its sphere of influence: annexing Crimea, intervening in Ukraine and Syria, and attempting to “bully” the Baltic countries of Latvia, Lithuania, and Estonia.

Last week, McConnell invited a bipartisan group of about 10 senators to have breakfast with the ambassadors and some legislators from the Baltic countries. All three countries belong to the West’s NATO military alliance, and so are guaranteed protection if they are attacked. But during the campaign, Trump questioned the NATO alliance.

McConnell wanted to leave the Baltic states in no doubt of the commitment to defend them from Russian interference, said those at the meeting.

“I doubt [McConnell] picked up the phone and called the president-elect to check whether that was something he wanted,” said Sen. Chris Coons (D) of Delaware, who was at the breakfast. “I think the majority leader showed a personal firm commitment to the independence of the Baltic states, period. And that to me was encouraging.”

Picking their spots

Crossing Trump could have political consequences. His tweets are searing, his base still highly energized.

“My head says that Republicans, particularly conservatives, will disagree with Trump when principles require it, perhaps on issues like infrastructure or trade,” says Republican consultant Matthew Mackowiak in an email. “But for a little while, they will be politically afraid of Trump, I suspect, as he has power, a huge platform, a willingness to criticize, and solid support among GOP primary voters.”

One area where some GOP senators feel confident that they will stand firm is if Trump overreaches on executive authority – further diminishing the power of Congress. They had enough of that under President Obama, even taking him to court, and before that, under President Bush.

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“I believe if President Trump does the same kind of executive overreach, that you will see a similar reaction because this is something if you care about the separation of powers, as a member of Congress, you have to be protective of the constitutional prerogatives of our branch,” says Sen. Susan Collins (R) of Maine.

Senator Collins did not vote for Trump. Instead, she wrote in Republican House Speaker Paul Ryan’s name.