It is hard enough to get voters to remember their names — there are nine Republicans running — in an election that is rife with confusion because of a delayed primary date and redrawn boundaries. And for all the hero worship Mr. Paul has cultivated among a small but vocal subset of the electorate, nobody is rushing to imitate “Dr. No.” “I don’t get a sense that people are looking for the next Ron Paul,” said Jay Old, a Beaumont lawyer and the top fund-raiser in the crowded field. “I think they are looking for people who want the very best for the district.” Partisan gerrymandering often turns political jurisdictions into zigzagging monstrosities, but the redrawn Congressional District 14 is straightforward and compact. It starts at the southeast corner of Texas, along the Louisiana border, and going west picks up two whole coastal counties, Jefferson and Galveston, and about half of another, Brazoria. It was not what Mr. Paul, the 76-year-old physician, had in mind. The district lost much of its rural character, and he faced the daunting prospect of introducing himself to about 300,000 people who were not in the old version of the district. Though he is running for president, Mr. Paul could have also legally sought re-election, as he did in 2008. Mr. Paul is now in his 12th term. He quit instead, and the race to fill his Republican-leaning seat has become a free-for-all among Republicans. If none of the nine candidates wins half of the vote outright on May 29, the top two will face off in a July 31 runoff. That appears to be the most likely scenario. Whoever emerges will probably face former United States Representative Nick Lampson, Democrat of Beaumont, who has strong ties to the area and an even stronger conviction that the seat will be competitive in the fall. There are 11 major party candidates altogether, plus Zach Grady, a Libertarian, running for the seat. There are four Republican candidates whose money and political connections give them the best shot at making a runoff. Mr. Old has raised the most money and had $308,000 on hand as of the last reporting period, which ended in April. He is already running TV ads, but his history of voting in past Democratic primaries and his donations to Democratic candidates have prompted criticism from his Republican opponents. Mr. Old, 48, said that Democrats traditionally dominated elections in his native Jefferson County, and that when there were no options in the Republican primary, “that means you pick the most qualified, most conservative candidate the other side offers.” Michael Truncale, another well-financed Republican from Beaumont, is stressing his grass-roots appeal and political reach as a State Republican Executive Committee member. At last count, Mr. Truncale, 54, a lawyer and former Texas State University System regent, had $149,000 in the bank. One possible factor working against both men is their home county: its tradition of voting for Democrats means Republican turnout could be much lower there than in the western part of the district. That is one reason State Representative Randy Weber of Pearland is expected to make the runoff. The owner of an air-conditioning company he started in 1981, Mr. Weber takes pride in his 2009 designation as the most conservative member of the Texas House, as scored by the Texas Conservative Coalition. He also picked up Gov. Rick Perry’s endorsement. “I have a track record of conservative action,” said Mr. Weber, who traces his political activism to former President Ronald Reagan’s re-election bid. “I don’t just know all the talking points. I’ve lived them for 29 years.” Mr. Weber had raised $282,000 for the race and had the second-highest cash-on-hand figure in the Republican field — $227,000, as of the last reporting period.