Democrats, still searching for a special election where they can chip into the Republicans’ House majority, caught a small break in South Carolina on Tuesday as they re-engaged in races underway in Georgia and Montana.

In South Carolina’s 5th District, which was held by Democrats before White House Budget Director Mick Mulvaney won it in 2010, tax attorney and former congressional aide Archie Parnell easily won the primary for a June 20 special — the same day as the pricey race in Georgia’s 6th District. Parnell, a first-time candidate, scored a 50-point victory over “resistance” candidate Alexis Frank, preventing the need for a May 16 runoff.

Republicans, meanwhile, watched two candidates score a near-tie, assuring a competitive runoff. State Rep. Ralph Norman (R-S.C.), who lost a race for the seat in 2006, will face State House Speaker Tommy Pope. Both candidates ran ahead of Chad Connelly, a former state party chairman running as an outsider, as well as a fringe candidate running on the restoration of the Confederate Flag.

For the next two weeks, Pope and Norman will compete for the nomination, a dynamic that Democrats hope can even out the campaigns’ bankrolls. In the last fundraising reports, Norman reported about $315,000 in fundraising, nearly matched by a donation from himself. Parnell had raised, and self-funded, only about half as much. Both candidates had raised more than Pope. As recently as last week, when Democratic National Committee Chairman Tom Perez spoke at the South Carolina party dinner, the party suggested that the race could break open if Parnell got enough opportunities.

“Democrats are ready to seize the opportunity to turn blue,” Perez tweeted Wednesday.

So far, the Democratic Congressional Committee has invested nothing in South Carolina — and Republicans have similarly stayed away. But as of Wednesday, the DCCC has put $1 million more into Georgia and $600,000 into Montana, where the national party had been criticized for not investing more, sooner, for candidate Rob Quist.

Montana’s election is the next on the calendar, with an unusual Thursday vote on May 25.