Sen. Ted Cruz of Texas declared on Twitter early Monday morning his candidacy for the White House, as fellow Sen. Rand Paul plans an ambitious five-state, five-day rollout of his own starting April 7 in his home state of Kentucky

Mr. Cruz is the first Republican hopeful to formally enter what is shaping up to be a diverse, crowded field for the party’s presidential nomination.

The Texas Republican was expected to formally announce his bid during a speech at Virginia’s Liberty University, the largest Christian institution in the country — a clear signal that the Texas Republican wants to solidify support among Christian conservatives as he builds his campaign, some analysts say.

Separately, The Washington Times has learned new details of Mr. Paul’s entry into the race, which campaign watchers say shows the financial heft and organizational skills the senator has assembled.

Mr. Paul will make his announcement first in Louisville at noon on April 7, then head to New Hampshire on April 8, Charleston, South Carolina, on April 9, Iowa City, Iowa, on April 10 and Las Vegas on April 11.

Presidential candidates traditionally enter the race by declaring in their home states and then flying to at least two of the first four states that hold presidential preference contests.

“It takes a significant campaign war chest and logistical planning and know-how to design and execute a three-state announcement tour,” said Michael Karem, whose experience in doing national campaign advancement extends back to Ronald Reagan’s first presidential nomination run in 1975.

The dual announcements bring into the race two of the most colorful and outspoken new figures in the party, each of whom has made his mark by leading a marathon filibuster on the Senate floor. Mr. Paul led a 13-hour talkathon in March 2013 to protest federal drone surveillance policies, while Mr. Cruz six months later held the floor for 21 hours in a bid to halt funding for Obamacare.

Both have strong tea party support, and both have wasted little time in shooting to prominence in conservative circles.

Mr. Cruz, 44, whose father was born in Cuba and who is the first Hispanic senator from the Lone Star State, has advanced his political profile significantly in just a few years. After serving as Texas solicitor general, he was elected to the Senate in November 2012 and has quickly emerged as one of President Obama’s fiercest critics on foreign policy, health care and a host of other issues.

But, with a penchant for challenging his party’s elders, Mr. Cruz faces a steep climb to capture the Republican nomination.

Polls show him far behind other likely candidates such as Mr. Paul, former Florida Gov. Jeb Bush and Wisconsin Gov. Scott Walker. He already is under attack from Democrats who want to paint him as a right-wing extremist.

Starting on the right

To win the nomination, however, he will have to move to the political middle and broaden his appeal, said Bruce Buchanan, a political science professor at the University of Texas at Austin who specializes in presidential politics.

“You start way right. That’s been his signature, and that marginalizes him for the mainstream of the Republican Party right now,” Mr. Buchanan said. “What might be in his mind is to use the tea party fervor to get early momentum, knock off challengers, diminish the field and then start thinking about actually trying to get the nomination.”

While Mr. Cruz entered the race on Twitter, Mr. Paul will advertise his campaign’s organizational prowess with the ambitious itinerary after his announcement in Kentucky.

The 52-year-old ophthalmologist was elected to the Senate in 2011. He has the support of many of the libertarian-mined conservatives who were devoted followers of his father, Ron Paul, also a physician and former congressman from Texas who built a loyal following for never deviating from conservative, free market, individual freedom principles during his long career.

Rand Paul has demonstrated his own clout among some of the party’s most dedicated activists. In February, he edged out Mr. Walker, Mr. Cruz and former neurosurgeon Ben S. Carson in the Conservative Political Action Conference straw poll.

Mr. Cruz and Mr. Paul will not have the official field to themselves for long. Mr. Bush and Mr. Carson have announced exploratory committees but have not formally declared their candidacies.

A CNN/ORC International poll released last week showed Mr. Paul among the early top tier of Republican Party hopefuls with Mr. Bush and Mr. Walker, while Mr. Cruz was far behind. Just 4 percent of Republican voters said Mr. Cruz would be their first choice for president.

Seven other Republicans finished ahead of Mr. Cruz, including Mr. Bush with 16 percent, Mr. Walker with 13 percent and Mr. Paul with 12 percent. Former Arkansas Gov. Mike Huckabee garnered 10 percent in the CNN/ORC poll.

Mr. Cruz has not received more than 6 percent in any Republican primary poll this year, according to Real Clear Politics data.

But Mr. Cruz appears to have a twofold strategy for improving his poll numbers and further establishing himself on the national stage.

First, he is staying in the spotlight by taking on the president on key foreign policy issues such as nuclear negotiations with Iran. In an interview with MSNBC last week, he said Republicans were to right to send a letter to Iran stressing that any nuclear deal with Mr. Obama would not last into the next administration.

“If we didn’t have a president like Barack Obama who routinely tries to circumvent Congress and the Senate when it comes to treaties, there wouldn’t be a need for a letter making clear that our Constitution gives Congress a vital role” in lawmaking, Mr. Cruz said.

The second part of Mr. Cruz’s strategy centers on competing hard for the Christian conservative vote that other candidates, such as Mr. Huckabee, a former Baptist pastor, also need to win.

“Sen. Cruz is probably one of the leaders, if not the leader, in the movement conservative leg of the Republican coalition. [Announcing at Liberty University] looks to me like a play to compete with Huckabee among the more socially focused conservatives, evangelical conservatives,” Kenneth T. Cuccinelli II, the former Virginia attorney general who ran unsuccessfully for governor in 2013, said Sunday on CNN’s “State of the Union.”

While Mr. Cruz’s first battles will be with fellow Republicans, Democrats are wasting little time in developing their own plans of attack.

Within hours of the news that Mr. Cruz would announce his bid Monday, the Democratic National Committee released a statement bashing the senator and suggesting that he doesn’t support Social Security or equal pay for women.

Mr. Cruz “led his party’s efforts to shut down the government in a personal crusade to take away quality health care from millions and to give control back to the insurance companies, and has been the embodiment of the Republican Party’s backwards policies that put millionaires and corporations first and the middle class last,” DNC press secretary Holly Shulman said.

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