The Affordable Care Act: The president can stop repeal of Obamacare, but a determined congressional majority can wreak havoc by using the initial budget process, known as reconciliation, which allows major changes to be made with only a majority Senate vote that isn't subject to veto.
"The Republicans can use reconciliation to pass lots of policies even repealing parts of Obamacare," says Lanhee Chen, formerly a top policy adviser to Mitt Romney and now a research fellow at Stanford University's Hoover Institution and a Bloomberg View columnist.
Republicans have struggled to come up with any palatable alternatives to the health-care law. That means major components such as the subsidies and tax credits, or the ban on discrimination against insuring those with pre-existing conditions, wouldn't be changed. But deep cuts in funding for running the program and getting new enrollees would take a toll.
"There could be a big hit in day-to-day administration," says Chris Jennings, a health-care expert who has worked with the Obama administration.
Fiscal Priorities: Despite the power of the presidential veto, all the compromises would move to the right. Congress would adopt measures closer to those favored by House Budget Committee Chairman Paul Ryan, cutting social spending for the poor and increasing defense spending.
Republicans would try to enact conservative tax measures. Reform of the corporate code might be a starting point, though changes to individual income taxes would be unlikely for budgetary and political reasons.
Regulation: A Republican Congress would hold the upper hand. Regulatory agencies the party doesn't like - a long list that includes the Consumer Financial Protection Bureau, the IRS, the Securities and Exchange Commission, the FDA, the EPA - could turn into toothless watchdogs with slashed budgets.
There would be a big push for the Regulations from the Executive in Need of Scrutiny Act, which requires congressional approval for all major regulations.
Appointments: Senate confirmation for all but the most routine nominations would be a slog. Republicans might repeal the so-called nuclear option rule, which requires only 51 votes (not 60 to break a filibuster) to confirm an executive or judicial appointment short of the Supreme Court.
It's difficult to envision a Republican-run Senate confirming any Supreme Court appointment by Obama.
Foreign Policy: The biggest issue might be a nuclear deal with Iran. Odds are the current negotiations will be extended until the end of this year or next year. For now, only the strong hand of Senate Majority Leader Harry Reid prevents legislation that might scuttle the negotiations from coming to the floor.
If a deal is reached, a Republican Congress would probably refuse to repeal the sanctions imposed on Iran. The president can waive some of these measures by executive order. But Congress would still have latitude to complicate any arrangement.
As to investigations of alleged administration misconduct, take the current number and double it. Democrats, when not in a state of panic, predict that such a scenario would lead to Republican overreach, paving the way for a Democratic president - and Senate - two years later. If so, the agenda of that new president would be to undo much of what had been done the previous two years.