Bachmann, a U.S. representative from Minnesota, won Saturday's Iowa straw poll, which claimed the first GOP casualty, Minnesota's former Gov. Tim Pawlenty.
Pawlenty, whose all-in campaign in Iowa never seemed to gain legs, announced Sunday on ABC's "This Week with Christiane Amanpour" he was dropping out of the Republican presidential sweepstakes.
Bachmann claimed 29 percent of the Iowa straw poll Saturday, with Ron Paul of Texas second at 28 percent. Pawlenty, who sank much time and money for a good showing in the poll, finished a distant third with 16 percent.
Pawlenty said during the ABC Sunday talk show his record as a two-term governor of Minnesota and what it meant for his qualifications to run the country never brought the lift he needed, "[so] I'm announcing this morning on your show that I'm going to be ending my campaign for president."
Bachmann, who traded verbal jabs with Pawlenty during last week's debate, said Sunday she had "great respect" for him and he brought an important voice to the campaign.
Bachmann attributed voter dissatisfaction with President Obama as a key component to her win.
"And I think what people see in me is that I'm a real person. I'm authentic," Bachmann said on "This Week." "And they want someone who's going to go to Washington and represent their values."
When pressed for what cuts she'd make to lower the federal deficit, Bachmann said she'd include entitlement programs in the mix.
"Right now, we're going to reform entitlements," she said. "We're going to reform them for anyone who's currently not on them."
She also said she wouldn't dismiss out of hand an openly gay or lesbian person as a member of a Bachmann administration, saying she would look for two things: Whether nominees would uphold the U.S. Constitution and whether they were competent.
"That's my criteria, nothing more," said Bachmann, who once characterized homosexuality as "personal bondage, personal despair, and personal enslavement."
The 2012 election was "really going to be an economic selection. People will want to know who can turn the country around," Bachmann said on CNN's "State of the Union." "That will be the big question."
Americans "want a change in Washington, D.C.," Bachmann said on "Fox News Sunday." "They don't want what [President] Barack Obama is giving, and I think we saw a punch to the gut in the United States this last week with what has happened in the economy."
U.S. and international stock indexes were on a steep roller-coaster ride last week in response to the Standard & Poor's downgrade of the U.S. credit rating.
Republican hopeful, businessman Herman Cain, told CNN his "middle of the pack [finish of 9 percent for fifth] … is what we were hoping to do" while conducting a slow-and-steady campaign to get his message out.
He said he didn't think the straw poll was a fair yardstick for reducing the GOP field.
"I call it a barometer. A better indicator would be the state-wide polls that they do with Iowa voters," said Cain, noting that in the last two Des Moines Register polls, he finished third.
Bachmann told CBS' "Face the Nation" she would be in South Carolina and New Hampshire "going person to person, voter to voter, state by state, to take my pro-growth, pro-jobs message. And as president of the United States, I will repeal Obamacare [the new healthcare law], and I will not rest until we do."
While winning the Iowa straw poll was gratifying, it still was a first step, Bachmann said on NBC's "Meet the Press.
"There's a lot of work to be done," she said. "I've only been in the race 48 days, so this is a tremendous accomplishment in that amount of time. I want to go back to Waterloo [where she announced her candidacy] where I was born and say thank you to the people of Iowa."