Mr. Faso was one of the architects of a plan that would have forced New York State to pick up the counties’ share of Medicaid financing — a proposal that was contained in an amendment to both the House and Senate versions of bills to repeal the Affordable Care Act, legislation that ultimately failed.
Only one of Mr. Faso’s Democratic challengers can claim government experience in New York; that candidate, Gareth Rhodes, who worked for the Cuomo administration, has sought to differentiate himself in a shoe-leather sort of way — or, more accurately, a tire-tread way.
Mr. Rhodes, 29, has set out to visit all 163 towns in a congressional district larger than Connecticut and Delaware combined, buying a Winnebago for the tour of an area that contains pristine horse farms and rod-and-gun clubs, art galleries and monster-truck shows.
Along with the pledge to visit every town is another campaign gimmick that Mr. Rhodes hopes will resonate in a district where the median household income is about $55,000. Wherever he goes, he asks for a donation of $19 (for the 19th District), an amount that he believes demonstrates support without straining wallets.
Mr. Rhodes is toward the back of the fund-raising pack, however. Occupying the lead in that race, according to campaign filings through the end of March, are Antonio Delgado, a former Rhodes scholar who lives in Rhinebeck and practices law in New York City, with $1.9 million, and Brian Flynn, an entrepreneur who became an activist after his brother was killed aboard Pan Am Flight 103 in 1988, with $1.4 million.
Patrick Ryan, a Kingston native, Iraq War veteran and small-business owner, had raised $1.3 million; David Clegg, a trial lawyer from Woodstock and member of several social-justice organizations, $650,000; and Jeff Beals, also of Woodstock, a high school teacher who was a C.I.A. intelligence officer and later a diplomat, $261,000. Mr. Rhodes’s year-end total was $450,000; his current total of $685,000, he said, includes the highest portion of small donations.
The lone woman in the race, Erin Collier of Cooperstown, who worked as an agricultural economist under President Obama, was a late entrant, so her fund-raising totals were not reflected in the last filing with the Federal Election Commission.
Steven Greenberg, a pollster with the Siena College Research Institute, said that once the Democratic candidate emerged in the June 26 primary, additional money would pour in.
“This is a district that is targeted by the Democratic Congressional Campaign Committee as one they would like to pick up, and it’s one of the key seats that the Republican National Committee wants to defend,” he said. “Both have made it clear that this will be a battleground district this fall.”
For his part, Mr. Faso defends his record as a freshman congressman, saying he has helped struggling dairy farmers in his district and secured projects and funding that are critical, if not sexy. He cited a hospital generator in Sullivan County and grants for sewer systems, as well as help he provided to individual constituents. “We fixed a disability claim for a veteran that was pending for 30 years,” he said.
As for the issue over which he and Gov. Andrew M. Cuomo have butted heads, the plan that would have forced the state to pick up counties’ share of Medicaid, Mr. Faso said he stood by the now-defunct legislation.
“The 57 counties outside of New York City spend more on Medicaid costs than the 49 other states combined,” he said. “This is a gigantic problem, which Governor Cuomo prefers not to address.”
Mr. Faso has tried to strike a balance in his stance on President Trump. And he has sought bipartisan solutions to problems through the House’s Problem Solvers Caucus, which is made up of two dozen Democrats and an equal number of Republicans. “I’ve said clearly when I agree and when I disagree with the president,” he allowed. “These are contentious and polarized times and I’ve tried to be a voice of reason.”
Most recently, in the wake of the school shooting in Parkland, Fla., Mr. Faso embraced such gun-control measures as tightening background checks, raising the age to buy a semiautomatic rifle and banning bump stocks.
Mr. Rhodes’s position on gun control is significantly tougher than that of Mr. Faso. At a recent meet-and-greet event at a home in this town in northwestern Sullivan County, he laid out a set of measures, including a ban on assault-style weapons like the AR-15, universal background checks and laws on gun storage and safety.
Mr. Rhodes grew up working on a farm in Ulster County that belonged to the Bruderhof religious community, where, he said, a “gun was a considered a tool, just like a tractor.” So he understands the culture protective of the Second Amendment, he said. “Here we are in Sullivan County, with 75,000 people and 25,000 pistol permits,” he said. “There are reasons people own firearms that go beyond hunting. I’m someone who is comfortable talking to sportsmen’s associations and rod-and-gun clubs.”
As a press aide to Mr. Cuomo, Mr. Rhodes crisscrossed the Hudson Valley in his first job after college. He left government in 2015 to enroll in Harvard Law School, and with only one semester left before graduating, Mr. Rhodes stepped away from Cambridge to run for Congress.
It remains to be seen whether his association with the Cuomo administration will help or hurt his candidacy. Four years ago, Mr. Cuomo took a beating in the district, drawing fewer votes than Zephyr Teachout in the Democratic primary and than Rob Astorino in the general election. (In 2016, Ms. Teachout unsuccessfully challenged Mr. Faso.)
Still, Mr. Rhodes trumpets his work for Mr. Cuomo, highlighting the agenda he helped promote.
“I was part of the administration that said no to fracking, and I’m proud to be from a state that did that,” he said to scattered applause at a recent campaign event here.
One resident asked Mr. Rhodes how his policies differed from those of his fellow Democratic challengers. Before he could finish his response, however, another attendee, Bruce Ferguson, who was a leader in the fight against fracking, piped up: “Electability, electability, electability.”
“Your work ethic is second to none,” Mr. Ferguson, a leader of a group called Sullivan Alliance for Sustainable Development, said to Mr. Rhodes. “You are up every morning and hitting the road. It’s the kind of energy we need to win a very tough race.”
Regardless of voter turnout in November, Mr. Faso will have the advantage of incumbency, not to mention a campaign war chest — currently at $1.7 million — that he can largely conserve until the general election draws closer, unlike his Democratic counterparts still seeking their party’s nod.
Gerald Benjamin, a professor of political science at the State University of New York at New Paltz, counts Mr. Faso as a longtime friend. A lifelong Republican, Professor Benjamin said he was so disturbed by President Trump’s record that he recently dropped his enrollment in the party. Yet he still plans to vote for Mr. Faso. “He’s deeply experienced, smart and wonky and totally informed on a range of issues,” he said.
Mr. Rhodes is nonetheless optimistic that voters will turn against Mr. Faso on issues ranging from health care to gun control, and expects that his own exhaustive tour of the district will win him votes. “This district is enormous: 7,900 square miles,” he told the small audience here. “I’m doing town-hall meetings. I’m going to diners, just listening. To me, this is important both to win the race, but also to take the voice of this community to Washington.”