The outcomes in Georgia and SC also could boost Republican efforts to advance health and tax legislation that has been bogged down by infighting and investigations into whether Trump's campaign colluded with Russian Federation in last year's presidential election.
The White House was quick to paint Handel's victory as a personal triumph for Trump.
However, the truth is a little more complicated than that.
Pelosi's allies have pointed out that numerous negative impressions that Republicans have of her are equally true of House Speaker Paul Ryan among Democratic voters. Of the 15 congressional districts with the highest levels of education, 13 are held by Democrats - Georgia's 6th District is one of the exceptions.
Rep. Tim Ryan (D-OH), who ran an unsuccessful campaign to unseat House Minority Leader Nancy Pelosi (D-CA) a year ago, said Thursday it will be hard for his party to take back control of the House with Pelosi at the helm. "Those voters came out of the hills". He also called on Democrats to cooperate with him, saying "Democrats would do much better as a party if they got together with Republicans on Healthcare, Tax Cuts, Security".
"They thought they were going to win last night in Atlanta", he said.
A lot of anti-Trump obstructionism is already in play, mostly by Democrats but also by Republicans, so if the GOP does lose its much-needed majorities, then Trump's administration will face even more difficulties in pushing through its policies.
She says Democrats "gave them a run for their money in all of them".
And after she predicted incorrectly that Democrats were poised to take back the House a year ago, some of Pelosi's colleagues feel that this time around, she needs to deliver.
But members of the rank-and-file are dissatisfied with that rationalization - and some are arguing for a new message and approach ahead of the midterms.
Congressman Bill Pascrell of New Jersey said, "A loss is a loss is a loss, and there's no excuses".
The Republican victory - the fourth special election won by the party this year - has generated renewed momentum for the party's long-awaited plan to repeal and replace Obamacare, with Senate Republicans due to unveil their own proposal for the American Health Care Act on Thursday.