Analysis by James A. Barnes

(CNN) -- Republicans were relieved when Debbie Lesko won a special election on April 24 to maintain GOP control of the Phoenix area congressional seat of former Rep. Trent Franks. Lesko's 52.4%-47.6% victory over Democrat Hiral Tipirneni — based on unofficial but near complete returns — was welcomed by Capitol Hill Republicans who were panicked after Democrat Conor Lamb won a House special election in March in Pennsylvania in a congressional district which, like Arizona's 8th Congressional District outside Phoenix, President Donald Trump carried handily in 2016. Both Franks and the Rep. Tim Murphy from the Pennsylvania district had resigned in scandal.

But an analysis of the special election returns from the 143 precincts that make up the congressional district in Arizona shows that Tipirneni performed better in many of the Republican-leaning precincts in the district, relative to results from the 2016 presidential election, than in its Democratic enclaves. This suggests that Tipirneni's message that Republicans are going to cut Social Security and Medicare to fill the yawning federal budget deficits exacerbated by the 2017 GOP tax cuts hit home with independent and even some GOP voters.

While many Democratic operatives have argued that the party's fortunes in the midterm elections in November will be determined by its ability to drive partisan Democrats to the polls -- making the midterms a so-called "base election"-- Tipirneni's performance suggests that a "persuasion" strategy with a message aimed at swing voters and disenchanted Republicans could also play dividends. Indeed, in GOP House seats that Hillary Clinton didn't win or even come to close carrying in 2016, a persuasion approach is probably critical.

We grouped precincts in Arizona's 8th Congressional District by the percentage of the major-party vote won by Hillary Clinton in the 2016 presidential election and compared that to how Tipirneni performed in those clusters of precincts in the 2018 House special election.

Where Clinton got less than 30% of the vote in 2016, Tipernini gained 11.1 percentage points. Where Clinton got more than 50% of the vote in 2016, Tipernini ganed less than 5 percentage points.

At the same time, the number of ballots cast in the Arizona special election in Republican-leaning precincts was higher relative to the number of ballots cast in 2016 presidential election, than in the more Democratic precincts. This is not surprising as Democratic turnout normally declines in non-presidential elections. So, while the turnout in this special election was generally higher in GOP precincts than in Democratic-leaning precincts, Tipirneni was nonetheless able to perform relatively better in those GOP outposts and was likely drawing support from independents and some Republicans with her persuasion efforts.

And Tipirneni's message on Social Security and Medicare was likely to play well in this suburban and exurban congressional district known for its burgeoning retirement communities.

Looking towards the midterm elections a CNN analysis of the demographics and politics of Republican-held congressional districts that most resemble AZ 8 produced the list below where a persuasion efforts by a Democratic candidate could score a win in November and include a few upsets:

Illinois 14 -- Incumbent: Randy Hultgren

Area: Northwestern Chicagoland: McHenry, Kane, Lake counties

Utah 04 -- Incumbent: Mia Love

Area: Central Utah: suburbs of Salt Lake City and Provo

Kansas 03 -- Incumbent: Kevin Yoder

Area: Kansas City metro

Washington 08 -- Incumbent: open

Area: Outer Seattle-Tacoma suburbs, central Washington

Georgia 07 -- Incumbent: Rob Woodall

Area: Northeastern Atlanta suburbs: Gwinnett, Forsyth counties

Virginia 10 -- Incumbent: Barbara Comstock

Area: DC and Virginia exurbs: Loudon, Fairfax counties, Winchester

Florida 06 -- Incumbent: Ron DeSantis

Area: North Central Coast: Daytona Beach, Palm Coast

California 25 -- Incumbent: Steve Knight

Area: Northern Los Angeles exurbs