WASHINGTON — Paul Ryan appears to be cruising toward re-election as House speaker, but his bold promise Tuesday of a new “dawn” for GOP unity — Republican lawmakers found “Make America Great Again” hats waiting on their chairs at a morning meeting — does not hide the deep divisions that remain.

There's a clash growing between Donald Trump's new vision of the Republican Party, which includes increased spending on several fronts, and budget hawks like Ryan and the GOP's small-government Freedom Caucus, whose ideology had previously dominated the party.

It's not just that the president-elect has promised costly big-ticket items — beefing up the military, building a wall along the border with Mexico and improving the social safety net, including health care.

Trump has also shown little interest in Ryan's signature budget-slashing proposals — such as cutting spending on Medicare and Medicaid — which had long been central to the GOP's plan for reducing deficits.

In fact, very little of what Trump promised to do during the campaign involved cutting government spending. Rather, he spoke of investing in the nation and creating jobs, and he once proudly proclaimed himself “the king of debt” in his business dealings.

House Republicans unanimously agreed Tuesday to nominate the Wisconsin Republican for another two-year term, rewarding his efforts to unify the party. The final House vote takes place in January.

But Ryan acknowledged that they are only beginning to work through the details of a unified Republican agenda.

“It's going to take time to figure out exactly what bill comes where and how it all adds up,” Ryan said.

The first clash may come over Trump's call for a $1-trillion infrastructure program.

Even if Trump relies on private investment, as his advisers have suggested, the notion of using government to prime the pump to create jobs stunned many conservatives when it received top billing on election night.

Dan Holler, spokesman at the conservative Heritage Action for America, was taken aback as he watched Trump's victory speech and the president-elect spoke of his “beautiful” program for new bridges, roads, airports and schools.

To many that sounded more like the dream of big-spending Democrats than the Republican just elected to the White House.

“It would be a mistake to think that's what the people were clamoring for,” said Holler, whose influential group tries to hold the line against spending. “As if that is the main message of the campaign — that we need a massive stimulus.”

The battle over spending is just one of the challenges that lie ahead as Republicans adjust to fact that they have now achieved what they long sought: Republican control of the White House and Congress for the first time in a decade.

Because Trump doesn't neatly align with any previous strain of the GOP, it will only confound the job facing congressional leaders.

In that sense, Trump's election won't end the civil war between Republicans on Capitol Hill. In fact, it may only complicate matters by adding a new front in their internal battle — a Republican-led White House.

lisa.mascaro@latimes.com