"I will not rest until Obamacare is repealed. You can take it to the bank," Bachmann, R-Minn., wrote on the microblogging service in a debate moderated by conservative political commentator Sarah Elizabeth Cupp and sponsored by the online Tea Party group, TheTeaParty.net.
"It's estimated to cost 800,000 jobs, is a small biz killer, and unconstitutional," Bachmann wrote in her 140 characters.
Businessman Herman Cain, former House Speaker Newt Gingrich, former New Mexico Gov. Gary Johnson, new entrant Michigan Rep. Thad McCotter and former Pennsylvania Sen. Rick Santorum also attacked the Patient Protection and Affordable Care Act President Barack Obama signed into law last year.
"Repeal & replace Obamacare and fully develop American energy. These would all create jobs by REDUCING govt.," Gingrich wrote when asked about how he would grow jobs.
The candidates answered a total of seven questions during the 90-minute live forum, responding with one to four messages known as tweets.
Asked how they would avoid continually raising the debt ceiling, Gingrich said: "We don't need Obama's 'balanced approach' (code for raise taxes). We need a balanced budget."
Santorum said, "Pass the Balanced Budget Amendment and work for its ratification across the country!"
Johnson posted: "By not incurring more debt! I'd submit 2 Congress a balanced budget in 2013, & veto any appropriation that exceeds that budget."
Cain said, "As President, I would focus on restructuring entitlement programs instead of reshuffling them."
Bachmann said: "Only way to avoid future increases is fund. change the way we spend. We must #cutcapbalance and repeal Obamacare."
McCotter said: "cut, cap & balance is the immediate solution to prevent a recurrence of the debt mess. The long term solution is not to simply."
McCotter had to finish his response in subsequent posts, The New York Times said.
Former Massachusetts Gov. Mitt Romney, former Minnesota Gov. Tim Pawlenty, former Utah Gov. Jon Huntsman and Texas Rep. Ron Paul did not participate.
On July 6 Obama responded to questions from Twitter users during the first Twitter Town Hall at the White House. He did not keep his answers to 140 characters.