Newly elected Rep. David Jolly downplayed the role Obamacare played in his campaign and warned fellow Republicans against obsessing about stopping President Obama's health care law.

Jolly, who narrowly beat Democrat Alex Sink in Tuesday's special election in Florida's 13th Congressional District, said the contest wasn't only a referendum against the Affordable Care Act, nor was it necessarily a bellwether for November's congressional elections.

"We had a local race," Jolly said on MSNBC's "Morning Joe" on Friday. "It's easy, either Inside the Beltway or just based on 30-second commercials, to suggest that [my campaign was] just a repeal [Obamacare] strategy. It never was in our race.

"And I'd say for Republicans, you know, that's an important lesson to hold on to."

Rather, Obamacare has become a "manifestation" of the public's fears of government intrusion, Jolly said.

"People see Obamacare as big government in their lives," he said. "It changes the role of government in their lives. That is what's resonating."

Jolly's comments differ somewhat from those of his new boss, House Speaker John Boehner, R-Ohio, who a day earlier suggested the GOP's long-standing opposition to the health care law will again be a central campaign strategy during the November elections. The speaker added that in the meantime, House Republicans won't back down from their repeated -- and failed -- attempts to repeal all or parts of Obamacare.

"Don't underestimate the amount of impact that Obamacare is having on the job market," Boehner told reporters Thursday.

But Jolly said the GOP also must come up with its own solutions and be willing to reach across the aisle and work with Democrats when possible.

"We can't be the 'party of no,'" he said.