Democrats already see signs of trouble clouding the prospects for common ground. As they seek to make permanent the Deferred Action for Childhood Arrivals program, or DACA, which grants protection to immigrants brought to the United States illegally as children, Mr. Trump is already imposing conditions that Democrats say they will not accept.

In a Twitter post on Friday, Mr. Trump said, among other things, that “Democrats have been told, and fully understand, that there can be no DACA without the desperately needed WALL at the Southern Border.” Democrats have consistently said that the Trump border wall funding is a nonstarter, and they are certain to object to his increasing insistence on ending other immigration programs they support.

As for infrastructure, a national program to rebuild the country’s aging transportation system has always been considered a prime opportunity for the two parties to come together to create jobs and bolster economic growth. But so far, Democrats note, the White House has been alone in developing an infrastructure plan that the administration says it intends to roll out in January. Top Democrats say it is not true bipartisanship to devise a major program, make it public and then expect Democrats to be won over by seeking adjustments as opposed to bringing in both sides from the start.

Other flash points could threaten bipartisanship. Senate Republicans and the White House remain frustrated with the pace of executive and judicial branch confirmations and would like to accelerate the process by slashing debate time for many nominees. The dispute could intensify as top appointees depart during the second year of the administration, putting new pressure on the Senate to fill those vacancies.

But Democrats, eying a potential Senate takeover, are not likely to want to give much ground on nominations if they stand to gain more control over who fills those jobs in 2019. If Republicans try to force the issue through a unilateral rules change, it is safe to say that would not help foster a bipartisan atmosphere.

In addition, Speaker Paul D. Ryan has suggested that Republicans might want to build on their tax overhaul success by pursuing changes in social spending programs that Democrats consider untouchable. Mr. McConnell, though, quickly put such topics off limits, saying that any changes in those programs would have to be done on a bipartisan basis — an impossibility given the Democratic refusal to go along.

Republicans are also counting on the new tax law to bolster their election prospects by putting more money in the hands of workers at the start of the year. But the law got off to a rocky start with confusion and anger around the country over whether homeowners could prepay their property taxes to avoid new tax limits, and Democrats will continue to pound that issue, angering Republicans.