ABC News’ Rick Klein reports:With Republicans grappling with the fallout of an intra-party battle that may have cost them a House seat, the head of the Senate Republican campaign effort is making a pledge that may ease some of the anger being directed at the party establishment. "We will not spend money in a contested primary," Sen. John Cornyn, the chairman of the National Republican Senatorial Committee, told ABC News in a telephone interview today. "There's no incentive for us to weigh in," said Cornyn, R-Texas. "We have to look at our resources. . . . We're not going to throw money into a [primary] race leading up to the election." Cornyn said his pledge extends to races for open Senate seats -- not incumbents who may face primaries next year. The NRSC so far has endorsed candidates in four open Senate seats -- Florida, Missouri, Illinois, and Pennsylvania. Cornyn's commitment is most immediately relevant in Florida, where the NRSC's candidate, Gov. Charlie Crist, is facing an aggressive challenge on his right from state House Speaker Marco Rubio. Some of the same conservative groups that supported Doug Hoffman in New York's 23rd congressional district are making noises about backing Rubio, in a contest that could be the next showdown over the direction of the party. "We're seriously looking at it. We like Marco Rubio a lot. We think that Charlie Crist represents some of the same things that Dede Scozzafava represents," Club for Growth President Chris Chocola said on ABCNews.com's "Top Line" Monday. Scozzafava was the Republican nominee in the New York race. Cornyn had praise for Rubio, and said he's sure that he would win the general election if he gets past Crist in the primary. Cornyn said he's confident that -- unlike in upstate New York -- Republicans will settle their differences in the primary. "The first lesson is that competitive primaries are generally a good thing," Cornyn said. "To me, that's the overarching lesson to be learned out of the 23rd. When 11 people get behind closed doors and pick the nominee ... the grassroots are going to find an alternative." Cornyn said the NRSC is only endorsing in races where -- like in Crist's case -- the candidate specifically requests its stamp of approval. He said that -- notwithstanding any endorsements -- his group would even offer advice on hiring and strategy to GOP challengers, like Rubio, who haven't been endorsed. Asked what endorsements mean, then, Cornyn said some candidates may want the backing to help line up support and financing. Beyond that, however, he said NRSC endorsements won't mean very much in practice. "Endorsements, frankly, are overrated.... They can to some extent be a negative," Cornyn said, noting that candidates in New Hampshire, California, and Colorado, for example, have asked the national party to stay out of their races. "People shouldn't read too much into endorsements by the NRSC. We are encouraging people we think are the strongest candidates to run." Cornyn said he hopes yesterday's results help expand Republicans' map next year: "There are a few other candidates I'd like to see get into these races. This can't be anything other than encouraging to them."