Mr. Sanford returned from a nearly weeklong disappearance in June to reveal he had been in Argentina to visit his mistress, a disclosure that led to questions about the legality of his travel on state, private and commercial planes.
At a news conference hours after fellow Republican Lt. Gov. Andre Bauer called for him to step down, Mr. Sanford said the people of South Carolina want to move past the scandals and that he will finish the last 16 months of his term.
"I'm not going to be railroaded out of this office by political opponents or folks who were never fans of mine in the first place," Mr. Sanford said. "A lot of what is going on now is pure politics, plain and simple."
Mr. Bauer and Mr. Sanford have served two terms together but were elected separately and have never been friends.
Some Republicans have been reluctant to seek Mr. Sanford's resignation or impeachment because they do not want to give Mr. Bauer what would amount to a long-term tryout for the job.
If Mr. Sanford steps down before his term ends in January 2011, Mr. Bauer said he will promise not to run in 2010 so that is not an issue. Mr. Bauer considered making the same offer in June but never officially did.
"The serious misconduct that has been revealed along with lingering questions and continuing distractions make it virtually impossible for our state to solve the critical problems we're facing without a change in leadership," he said Wednesday.
House Republicans are expected to discuss impeachment this weekend. The House will likely launch those proceedings when lawmakers return for their regular session in January, though they could also hold a special session before then. Any House member can file a bill to impeach.
Mr. Sanford said heeding Mr. Bauer's call to resign would be like "heaven on earth" because it would get him out of the public eye, but it would not be right.
"Me hanging up the spurs 16 months out, as comfortable as that would be, as much as I might like to do that on a personal basis, it is wrong," he said.
Mr. Bauer said he tried to give Mr. Sanford the benefit of the doubt after he admitted his affair, but the state has been paralyzed by questions raised afterward about the legality of his official travel. Mr. Bauer said he is concerned that calls for Mr. Sanford's impeachment will dominate next year's legislative session instead of issues like the economy and job creation. Mr. Bauer said he will go ahead with his candidacy if Mr. Sanford does not resign or lawmakers do not return to Columbia to force him out within 30 days. Term limits bar Mr. Sanford from a third term.