Story highlights Cheney releases a statement citing "serious health issues" in her family

Wyoming Sen. Mike Enzi first won the Senate seat in 1996

The contest caused bitter feelings in the Republican Party and the Cheney family

Enzi and Cheney speak by phone; he says he respects her decision

Liz Cheney, whose upstart bid to unseat Wyoming Sen. Mike Enzi sparked warfare in the Republican Party and within her own family, is dropping out of the primary race, she said on Monday.

"Serious health issues have recently arisen in our family, and under the circumstances, I have decided to discontinue my campaign," the eldest daughter of former Vice President Dick Cheney said in a written statement.

Cheney, 47, began telling associates of her decision over the weekend, CNN reported Sunday night.

She was not specific about the health issues involved in her decision. But CNN has learned from multiple sources close to the family that they involve at least one of her children.

"Though this campaign stops today, my commitment to keep fighting with you and your families for the fundamental values that have made this nation and Wyoming great will never stop," she added.

Cheney called Enzi, 69, about her decision to bow out.

"I talked to her first thing this morning. It was very nice that she called me," he told CNN on Capitol Hill, adding that he respects Cheney's decision and that "she and her family are in our prayers."

Asked if he was relieved that she was no longer in the race, he said he hasn't "had a chance to reflect on that yet."

Cheney's surprising decision to jump into the race, an announcement made in a YouTube video last summer , roiled Republican politics in Wyoming, a state that her father represented in Congress for five terms in the 1970s and 80s.

Enzi is a low-key presence in Washington in the Senate. He was elected in 1996 and has amassed a conservative voting record with few blemishes.

He expressed public annoyance at Cheney's decision to mount a primary challenge.

A number of his Senate colleagues quickly rallied to his side and pledged support for his re-election bid.

There was little public polling of the race, but two partisan polls released last year showed Enzi with a wide lead, an assessment mostly shared by GOP insiders watching the race.

In a statement after her announcement to drop out, the Wyoming Republican Party praised Liz Cheney for being a "stalwart supporter" and fundraiser for Wyoming candidates and county parties in the past.

"Liz is a rising star in Wyoming and national politics and we look forward to her return when the time is right for her and her family," the statement read.

Cheney's campaign got off to a rocky start.

Her critics labeled her a carpetbagger, noting that she moved to Wyoming only in 2012 after relocating from Virginia. The issue flared in August after the Wyoming media reported that Cheney improperly received a fishing license despite not living in the state for at least a year, as the law requires.

Grabbing even more attention was her very public dispute with her sister, Mary, over the issue of same-sex marriage.

Mary Cheney, who is a lesbian, took to Facebook in November to object to Liz Cheney's opposition to same-sex marriage, claiming that her sister has previously supported her relationship while saying something very different on the campaign trail.

The dispute prompted their parents to weigh in, saying they were "pained" to see the sisters battle over a private matter in full view of the news media.

Beyond the campaign missteps, Cheney's election effort, vigorously supported by her father and his allies, often felt out of tune with the small-government conservative sentiment that has fueled other Republican primary challengers.

Cheney, like her father, is an unapologetic neoconservative who favors muscular use of American military power overseas, a policy that does not sit well with many grassroots conservatives, particularly in the libertarian-leaning West.