Early last year, Jack Fields -- a model young Texan, then 27, applecheeked, athletic, newly married, and as conservative as the day is long -- decided to make his first race for political office.

He wasn't given much of a chance.

For one thing, he was aiming high: at seven-term Democrat Bob Eckhardt's seat in Congress. For another, there was already another conservative Republican in the race who was older and better connected. But, undaunted, Fields and his bride, Roni Sue, began knocking on doors and recruiting precinct captains.

Today Jack Fields is running a campaign that reportedly will spend half a million dollars by election day.

Gerald Ford and Jack Kemp, among other Republican luminaries, have personally campaigned for him. He has held Washington fund-raisers. He has an expensive television advertising campaign, partly produced and shot in Washington. He is even given a good chance of unseating Eckhardt.

His success is due in large part to his own persistence. But he is also a case study in the way enormous amounts of money and expertise can be mobilized on a national level to help an unknown local candidate for Congress -- especially if the candidate is a conservative Republican.

Fields and others like him around the country have more such resources available to them this fall than congressional candidates have ever had.

For years Eckhardt has attracted serious opposition, although never anyone as well financed as Fields. Eckhardt, a scholarly liberal who votes with East Coast Democrats on energy issues, regularly infuriates the oil and gas establishment of Houston, in which half his district lies.

In the spring of 1978, Lloyd Pierson, the administrative assistant to Bill Archer, the conservative Republican congressman from the district next to Echkhardt's, went home to Houston to run for the seat. Because of his strong ties to downtown business, Pierson was considered the favorite for the Republican nomination. Nobody paid much attention to Fields, who had just graduated from law school and moved back to his hometown of Humble, Tex., to join the family cemetery business.

Early in 1979, Fields -- who cancelled several scheduled interviews for this article -- came to Washington and called on Paul Weyrich, the director of the Committee for the Survival of a Free Congress, a leading New Right political action committee. Weyrich liked what he saw.

In the fall, Fields came up again to attend Weyrich's week-long training school for prospective congressional candidates. Pierson came too, but he left before the school ended. Weyrich decided he didn't like Pierson.

"Pierson just sort of . . . took a very casual attitude toward us, like we didn't matter," says Weyrich, grinning mischievously. "But I guess we did." When the school ended, Weyrich called several New Right congressmen whom he had called on for help. "I told them, 'Look, you may not want to get involved in this race because I think Jack Fields is the more attractive candidate.'" Weyrich says.

In October 1979, Pierson dropped out of the race and Fields officially announced his candicacy.

Other New Right groups quickly came into the fold, Moral Majority gave Fields $1,000. The Conservative Victory Fund had given him $2,000 and contributed a free mailing. The National Conservative Political Action Committee plans to give Fields the legal limit of $5,000 and will pass on to him, without charge, the results of a poll it commissioned.

Having won the hearts of the New Right, Fields then got the support of a second important national constituency: the Republican Party.

As early as the spring of 1979, a field organizer from the National Republican Congressional Committee went to Humble and met with Fields, In October 1979, the NRCC named him to its "National Congressional Council," a group of 40 candidates who attended yet another how-to-run school in Washington.

In addition, the NRCC will give a total of $80,000. It educated his press secretary at a press secretaries' school, and his campaign manager at a campaign mangers' school. In its fulldress video production unit, new this year, it cut a series of campaign spots for him and placed them on Houston television. Like the New Right groups, it gave Fields extensive briefings and printed material on issues.

An NRCC field organizer has visited Fields' district a half-dozen times this year and is in touch with the campaign by phone on a weekly basis. And, largely through the NRCC's good offices, Fields got $4,000 from the Republican National Committee and $5,000 from the Texas Republican Congressional Committee.

In April of this year, the NRCC gave Fields a luncheon at a Houston hotel, at which its chairman, Rep. Guy Vander Jagt (R-Mich.), and John Connally spoke. After Fields spoke on various national issues, Vander Jagt told reporters that he had described "the Republican budget position better than many Republican congressmen can."

Partly on the strength of the New Right and party support, Fields then won over a third national constituency, the business political action committees (PACs).

In February 1980, the U.S. Chamber of Commerce sent someone to the district to look Fields over. In August, the chamber endorsed him. It sent a message urging contributions to its 200 members in the district -- a new practice this year -- and put Fields on its national "opportunity list." The chamber also has helped Fields on issue research; last week, for instance, it sent two staff members to Humble for that reason.

And this May, the National Association of Manufacturers sent a man to see Fields, out of which came a flattering profile in "PAC Manager," a NAM publication sent to people who make corporate political-spending decisions. "PAC Manager," too, is new in the last year.

The approval of the chamber and the NAM helped Fields with PAC money, but he would have done well there anyway. His campaign sends periodic "PAC Summary" bulletins to PAC managers around the country, and the PACs have, as one national Republican official puts it," started to beat a path to his door."

Because of his strong local roots and the odiousness of his opponent to conservatives, Fields has been able to tap all the national networks of funding and other help better than all but a handful of congressional candidates. His political stands, conservative on such economic issues as taxes and the budget and on such social issues as abortion, school prayer and busing, make him attractive to the entire spectrum of national conservative groups.

He has also strongly stressed local issues, and in particular his family connections in and loyalty to the district. Because of redistricting, Eckhardt's house is actually in the next district over, and his heart, Fields often says, is here in Washington.

Ten or even five years ago a candidate like Fields could not possibly have drawn such strong national support. There were only 89 corporate PACs in January 1975: there are more than a thousand today. Most of the New Right groups are creatures of the 1970s, and have grown particularly fast in the last three years. And the Republicans have become much more sophisticated in helping local candidates in just the last few years, especially in the use of political media.

The Democrats and nonparty liberal groups have lagged badly in all those areas. Last week, the Federal Election Commission estimated Democratic spending on congressional races this year at $1.3 million, and Republican spending at $16.3 million.

In addition, as the conservative groups have grown they have tended to cross-fertilize one another. For example, several of Fields' most important Washington supporters said they found out about him at a regular luncheon held every other Monday at the Key Bridge Marriott and attended by about a dozen heads of PACs.

One such supporter is Terry Dolan, the 29-year-old director of the National Conservative Political Action Committee, which spent $350,000 in the 1978 elections and will spend $3 million to $4 million this year.

"Good candidate," Dolan says of Fields. "Conservative beliefs. The race is eminently winnable, and frankly, it's just a function of money."