President Donald Trump speaks to the media as he departs for a campaign rally in Fort Myers, Florida, on the South Lawn of the White House in Washington, October 31, 2018.

Republicans apparently lost the House but held onto the Senate in midterm races, promising President Donald Trump's economic programs are likely to remain in tact.

The newly empowered Democrats are likely to have a fractious relationship with the president, do not see eye to eye with many of his policies — and they may try to impeach him.

"I think there could be much clearer tension," said Tom Block, Washington policy strategist at Fundstrat. "They're going to subpoena Trump's tax returns. That could go all the way to the Supreme Court. In the short term, there's going to be no change to the economic policy. The good economy is baked in for the next 12 months and with the divided government, there could be an infrastructure bill."

Stock futures were firmer Tuesday night, but well off highs reached when it looked like Republicans had a chance of holding onto the House. Treasury yields were lower, and the dollar gave up its early evening gains and was lower against the euro.

"It's certainly not the blue wave Democrats were hoping for," said Jack Ablin, chief investment officer at Cresset Wealth Advisors. "Based on what we're seeing right now, the stock market is liking it. History has shown that the mixed party control is generally the best combination. This is as close to market expectations as we're likely to see."

But Ablin also cautioned that Democrats could be tough on Trump. "Is it impeachment or infrastructure?" he said.

"I think it's a disappointing night for the Democrats, certainly in the Senate. It's not a disaster," said Greg Valliere, chief global strategist at Horizon Investments. "One underestimates Donald Trump at one's own peril. He made the Senate his priority, and this looks like a surprisingly strong showing for Republicans in the Senate."

Dan Clifton, head of policy research at Strategas Research, said Trump is motivated to continue driving policies that boost the economy, with his own re-election now in sight.

"Starting tomorrow, the president is going to start thinking about his own election and he's going to see his party struggled a bit in the suburbs," said Clifton.

For that reason, he may try to resolve trade tensions with China, and show some progress when he meets with China President Xi Jinping at G-20 at the end of the month.

"A win is a win, and it's coming in pretty big," said Clifton. "That allows them to stand up there and say we now have a mandate from the American people for oversight of this president and his policies. That kind of starts everything off. [Democrat Rep. Nancy] Pelosi is going to have to figure out what she wants her accomplishment to be. You just can't investigate and beat up. At some point they're going to have to make a decision — results or resistance."