Lynchburg, Virginia (CNN) Sen. Ted Cruz, the conservative firebrand from Texas, became the first Republican to announce his campaign for the presidency, and he spent Monday morning telling a crowd at the largest Christian university in the world to imagine what the country will be like when he takes office, and pitching his personal history as a key part of his campaign.

"These are all of our stories," Cruz told the audience Monday, roaming around the circular stage at Liberty University, in Lynchburg, Virginia, opening his remarks by spotlighting his family history and his own path to Washington. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant."

Cruz drew on the past only to focus on the future, repeatedly and emphatically asking the Liberty University student audience to "imagine" the U.S. under conservative leadership -- laying out his vision for the country and a Cruz presidency.

The senator from Texas, who burst into the national limelight with his staunch opposition to Obamacare and his willingness to shut down the federal government, presents a direct challenge to the expected bids of establishment Republicans such as Florida Gov. Jeb Bush -- candidates Cruz coyly refers to as the "mushy middle."

Monday's event was the last part of a carefully coordinated media rollout, following Cruz's announcement of his candidacy in a 30-second video message posted on Twitter shortly after midnight on Monday, roughly 24 hours after the Houston Chronicle first reported his planned announcement.

Ten thousand students from Liberty University crowded into the university's main arena for Cruz's announcement. The venue choice at this socially conservative campus aims to give Cruz an early boost among evangelical voters, who will be key to boosting presidential hopefuls in states like Iowa and South Carolina that have early nominating contests. It was a youthful crowd, as students are required to attend the University's tri-weekly convocation address.

Not all in the audience were guaranteed Cruz supporters: Several attendees sported red "Stand with Rand" shirts, repping Kentucky Republican Sen. Rand Paul, who is slated to announce his candidacy early next month.

Jerry Falwell Jr., the university's president and son of its founder and evangelical icon, introduced Cruz as a senator who "has gone against the tide" and a "man of great character," all while stressing that the university does not endorse candidates for office.

Falwell picked up on Cruz's assertion that millions of evangelical Christians did not vote in 2012, pointing out that "if any candidate can energize that group, it will make a huge difference in any national race."

Asked after the speech how he prepared for the event, Cruz said he "spent some time in prayer" thinking about the message he wants to convey.

"At the end of the day it's listening to the people about the vision for turning the country around," Cruz told CNN, adding that he was "incredibly" encouraged and inspired by the support.

Sen. Ted Cruz brings his daughters, Catherine, right, and Caroline on stage during a walk-through for his announcement.

Cruz's announcement came on the five-year anniversary of the passage of the Affordable Care Act, also known as Obamacare, which Cruz has fought in the Senate to repeal. Cruz marked the anniversary by pledging to repeal "every word" of the healthcare law as president.

Cruz also jabbed at Common Core education standards -- which Bush supports -- and repeated his pledge to abolish the IRS, instead suggesting Americans could file their taxes on a postcard.

And Cruz drew the longest and loudest applause from the audience when he prompted the audience to "imagine a President who stands unapologetically with the nation of Israel."

Cruz's advisers envision a three-pronged strategy that focuses on dominating the tea party faction and competing in the libertarian and Christian conservative circles.

A constant and vocal critic of the Obama administration, Cruz is perhaps best known for his stalwart fight against Obamacare in 2013, which led to a tense standoff between Democrats and Republicans and ultimately resulted in a 17-day government shutdown. The showdown was punctuated by Cruz's 21-hour speech on the Senate floor

While popular in conservative and tea party circles, Cruz has a long way to go in terms of broader support in the GOP base, according to public opinion polls. A CNN/ORC International survey conducted this month on the hypothetical Republican primary showed Cruz came in with 4% support among Republicans and independents who lean Republican.

But the field is still relatively open, with the top contender -- Bush -- coming in at 16% support, followed by Scott Walker at 13%.

But Cruz has relatively strong favorability numbers. According to a recent Quinnipiac University poll, he is viewed in a positive light by 45% of Republicans, compared with only 8% who don't have a favorable opinion of him. Still, 46% say they haven't heard enough about him to form an opinion.

Photos: Moments from Ted Cruz's career U.S. Sen. Ted Cruz, a Republican presidential candidate, speaks during a campaign rally at the Indiana State Fairgrounds on Monday, May 2. Hide Caption 1 of 24 Photos: Moments from Ted Cruz's career Cruz holds up the hand of Carly Fiorina at a campaign rally in Indianapolis on Wednesday, April 27. Cruz named Fiorina, a former presidential candidate, as his running mate. Hide Caption 2 of 24 Photos: Moments from Ted Cruz's career Cruz celebrates his Wisconsin primary win with his wife, Heidi, and Gov. Scott Walker in Milwaukee on Tuesday, April 5. Walker endorsed Cruz for the presidency. Hide Caption 3 of 24 Photos: Moments from Ted Cruz's career With his wife by his side, Cruz tours the Dane Manufacturing facility before speaking to workers in Dane, Wisconsin, on Thursday, March 24. Hide Caption 4 of 24 Photos: Moments from Ted Cruz's career Cruz speaks during the CNN Republican debate in Miami on Thursday, March 10. Hide Caption 5 of 24 Photos: Moments from Ted Cruz's career Cruz and his wife wave to the crowd at Liberty University after he announced his presidential candidacy in Lynchburg, Virginia, on March 23, 2015. Hide Caption 6 of 24 Photos: Moments from Ted Cruz's career Cruz speaks during the 2013 NRA Annual Meeting and Exhibits at the George R. Brown Convention Center on May 3, 2013, in Houston, Texas. Hide Caption 7 of 24 Photos: Moments from Ted Cruz's career Cruz poses with his wife, Heidi, and his daughters Caroline and Catherine. Hide Caption 8 of 24 Photos: Moments from Ted Cruz's career Cruz (left) fields questions from Bruce Rastetter at the Iowa Ag Summit on March 7, 2015, in Des Moines, Iowa. The event allows the invited speakers, many of whom are potential 2016 Republican presidential hopefuls, to outline their views on agricultural issue. Hide Caption 9 of 24 Photos: Moments from Ted Cruz's career Nobel Peace Laureate Elie Wiesel (left) listens as Cruz (right) speaks during a roundtable discussion on Capitol Hill March 2, 2015 in Washington, D.C. Wiesel, Cruz and Rabbi Scmuley Boteach (center) participated in a discussion entitled 'The Meaning of Never Again: Guarding Against a Nuclear Iran.' Hide Caption 10 of 24 Photos: Moments from Ted Cruz's career Governor Greg Abbott (center) speaks alongside Cruz (left), Attorney General Ken Paxton (right) at a joint press conference February 18, 2015, in Austin, Texas. Hide Caption 11 of 24 Photos: Moments from Ted Cruz's career Sen. Patrick Leahy (right) escorts Loretta Lynch back from a lunch break as Cruz (left) sits nearby during her confirmation hearing before the Senate Judiciary Committee January 28, 2015, on Capitol Hill. Hide Caption 12 of 24 Photos: Moments from Ted Cruz's career Cruz greets supporters at the South Carolina Tea Party Coalition convention on January 18, 2015, in Myrtle Beach, South Carolina. A variety of conservative presidential hopefuls spoke at the gathering on the second day of a three-day event. Hide Caption 13 of 24 Photos: Moments from Ted Cruz's career Cruz (left) and then-Texas Governor Rick Perry stand together during a press conference at the front gate of Fort Hood about Iraq war veteran, Ivan Lopez, who killed three and wounded 16 before taking his own life on April 4, 2014, in Fort Hood, Texas. Hide Caption 14 of 24 Photos: Moments from Ted Cruz's career (Left to right) Sen. Lindsey Graham, Sen. John McCain and Cruz listen as President Barack Obama delivers the State of the Union address on January 28, 2014, in Washington, D.C. Hide Caption 15 of 24 Photos: Moments from Ted Cruz's career Then-Senate Minority Leader Mitch McConnell (second right), poses with Republican senators-elect Jeff Flake (left), Deb Fischer (second left), and Cruz (right) at the U.S. Capitol on November 13, 2012, in Washington, D.C. Hide Caption 16 of 24 Photos: Moments from Ted Cruz's career Cruz speaks to reporters on September 25, 2013, after ending his talk-a-thon on the floor of the US Senate in Washington, D.C. Hide Caption 17 of 24 Photos: Moments from Ted Cruz's career Cruz speaks as then-Rep. Michele Bachmann (left), Sen. Mike Lee (second right) and Sen. Rand Paul (right) listen during a news conference May 16, 2013, on Capitol Hill. Hide Caption 18 of 24 Photos: Moments from Ted Cruz's career Cruz listens to testimony during a Senate Judiciary Committee hearing on April 22, 2013, in Washington, D.C. Hide Caption 19 of 24 Photos: Moments from Ted Cruz's career Cruz holds a news conference to announce the plan to defund Obamacare on March 13, 2013. Hide Caption 20 of 24 Photos: Moments from Ted Cruz's career Cruz speaks at the CPAC on March 6, 2014, in National Harbor, Maryland. Hide Caption 21 of 24 Photos: Moments from Ted Cruz's career Then-Senate Republican Candidate and Texas Solicitor General Cruz speaks at the 'Patriots for Romney-Ryan Reception' on August 29, 2012, in Tampa, Florida. Hide Caption 22 of 24 Photos: Moments from Ted Cruz's career Then-Senate Republican Candidate and Texas Solicitor General Cruz speaks during the Republican National Convention at the Tampa Bay Times Forum on August 28, 2012. Hide Caption 23 of 24 Photos: Moments from Ted Cruz's career Then-Senate Republican Candidate and Texas Solicitor General Cruz speaks during the Republican National Convention in 2012. Hide Caption 24 of 24

Jason Miller, an adviser to Cruz's campaign, confirmed that the campaign's fund-raising target is $40 million, and the campaign believes it can raise $1 million in the first week.

Cruz this month finished an early-voting state tour to Iowa, South Carolina and New Hampshire -- and he's scheduled to return to New Hampshire on March 28 to speak at a brunch in Rockingham County . Depending on the Senate schedule this week, he could possibly make more early-state trips, according to advisers.

After his speech Monday, he'll head up to New York for media appearances and a fund-raiser.

Cruz developed a loyal following when he won his 2012 primary battle in Texas as a little-known candidate, forcing then-Lt. Gov. David Dewhurst into a surprise runoff and ultimately defeating the establishment Republican.

Along with two other first-term senators who are expected to run for president (Rand Paul and Marco Rubio), Cruz will likely face questions over experience, an issue that Republicans brought up in 2008 against Barack Obama, who was also a first-term senator at the time.

Before running for the Senate in 2012 -- his first campaign for public office -- Cruz was solicitor general of Texas and argued before the Supreme Court. He graduated from Princeton University and Harvard Law School.

Cruz was swarmed by students and reporters after he descended the stage and started to exit the arena. He took photos and signed autographs for about a half hour, as his team tried to escort him through the crowd.

One girl who was raising money selling baked goods offered to give Cruz a dozen cupcakes for free but he pulled out his wallet and gave her $20.

A pair of enthusiastic sisters shouted out to Cruz to tell him that, like his own daughters, they were also named Caroline and Catherine and were two years apart.

"That's just cool," he said, as he gave them both high fives. "That is awesome."

One student who said she was Hispanic said she and her whole family were behind him. "You have the Hispanic vote," she joked, then proceeded to start talking to him Spanish.

While Cruz's father is Cuban, he's not fluent in Spanish.

"We grew up speaking Spanglish. My grandmother would be like 'Nino, throw me the remote control'," he said This is who we are as a people. We got to tell that story," Cruz said.

