U.S. Senator Ted Cruz pauses to look at the crowd as he confirms his candidacy for the 2016 U.S. presidential election race during a speech at Liberty College in Lynchburg, Virginia, March 23, 2015. Reuters/Chris Keane

Republican Sen. Ted Cruz has shattered his fundraising goals for his presidential campaign set for its first week, raising $4 million in the eight days since he declared his candidacy for the 2016 GOP nomination.

“Often you have an establishment candidate, usually the moderate, who will be well funded,” Cruz spokesman Rick Tyler told the Wall Street Journal. “Here we have a candidate who is conservative and can raise money.”

Cruz's campaign is targeting grassroots voters, rather than wealthy, large-scale donors. His spokesman told the Journal that 95 percent of the donations raised since he announced his candidacy were contributions of $100 or less. The average donation was about $83.

The campaign's initial target was to raise $1 million in its first week.

Cruz aims to raise around $40 million in the next year, a figure that is expected to be dwarfed by the money raised by Jeb Bush, who has the benefit of an established network of major donors who supported his father, brother, and failed 2012 Republican candidate Mitt Romney.

"Jeb Bush will shatter every fundraising record ever set. They've set a goal this first quarter of raising $100 million. It wouldn't surprise me if Jeb does much more than that, if he blows past $100 million," Cruz told the Washington Post.

Since declaring his candidacy on March 23, Cruz has been targeting small donors with an email campaign. His campaign sent out at least three emails in two days last week, appealing for “emergency” contributions to fight “constant attacks” from “liberals,” who the campaign said were “out for blood,” according to Bloomberg.

Following two consecutive presidential election defeats, in which President Barack Obama's campaign managed to successfully out-fundraise his opponents, Republicans are increasingly focusing on digital fundraising platforms, experts say.

“Republicans who are used to raising money on Wall Street and wherever else, they are going to be finding that using the Internet and banding together repeat $10 donations and selling products like t-shirts is going to be another very effective way to not only raise money, but to keep people engaged,” Vincent Harris, chief digital strategist for Rand Paul’s 2016 team and a former digital operative for Ted Cruz, told the IndyChannel.

In addition to Bush, Cruz faces an uphill battle against other GOP hopefuls, including Kentucky Sen. Rand Paul, and New Jersey Governor Chris Christie.