Currently, Republican George W. Bush leads Democrat Al Gore in Florida by 383 votes, according to an unofficial tally by Voter News Service, of which CBS News is a member.
In New Mexico, a 500-vote oversight could swing the state back in favor of Vice President Al Gore, according to an Associated Press tally. The county where the error was found has not certified the new results, and the overall recount in the state continues.
After days of keeping a low - if not invisible profile - a smiling Gore emerged from the White House to tell Americans to be patient as the recount saga unfolds.
"Having enough patience to spend the days necessary to hear exactly what the American people have said is really the most important thing," the vice president said in a brief statement outside the White House, who proclaimed that the "integrity of our democracy" is at stake.
Taking no questions, Gore justified the additional time taken in the recount, saying it's important that "every vote is counted and counted accurately."
"I would not want to win the presidency by a few votes cast in error, or misinterpreted, or not counted - and I don't think Governor Bush wants that either," said Gore, referring to his Republican rival from Texas.
In Austin, Tex., Bush spokeswoman Karen Hughes said all of America wants a fair and accurate count in Florida, but added a hand recount of the ballots can't produce that result.
"The vice president basically said we should ignore the law so he can overturn the results of this election," Hughes asserted. Bush spent the day at his ranch near Crawford, Tex. and made no public appearances on Monday.
Earlier in the day, legal wrangling over the election moved forward on three politically divergent fronts in Florida.
At issue: hand recounts of vote tallies in four Democratic-leaning counties in the Sunshine State: Volusia, Palm Beach, Broward and Miami-Dade.
On one legal front, a federal judge denied an effort by Bush's campaign to stop all the recounts in those selected counties.
At a Miami hearing prior to issuing his ruling, U.S. District Judge Donald Middlebrooks told lawyers for both sides that he wanted to "get it done quickly," adding he knew his decision - which could favor Gore's chances to be declared the ultimate winner in Florida - would be appealed.
"I am not under an illusion I am the last word on this, and I am rather grateful for that," Middlebrooks said.
Bush campaign's can appeal the decision, but has not said whether it will.
Also, a Democratic-backed effort by one of those four counties to extend Tuesday's recount deadline made its way to Florida state court.
Still in the midst of its hand balot recount, Volusia County sued in state court for the right to complete and certify its manual count, as well as to bar state officials from ignoring the county's results regardless of Tuesday's deadline of 5 p.m. Eastern. Florida Secretary of State Katharine Harris imposed that cut-off time for all of the state's 67 counties to certify their election results.
"The process of counting and recounting the votes cast on Election Day must end," she said in Florida's capital of Tallahassee.
Gore's top recount adviser Warren Christopher denounced Harris' move as "arbitrary and unreasonable"
The ex-diplomat suggested the decision - which Harris said was fixed by Florida law - was politically motivated, in part because it has the "look of an effort to produce a particular result."
"We believe down deep," he said, "that if the view of the Florida voters is truly known, it will turn out that Al Gore has more votes than others here in Florida."
And, noting that Harris had campaigned for Bush and is a supporter of the candidate's brother - Florida Governor Jeb Bush, who has recused himself from the recount process - Christopher said of her, "Her statement has to be taken into that context."
In its first legal salvo on the election dispute, Gore's campaign joined Volusia County's lawsuit on Monday, indicating that it will seek temporary restraining orders for the other counties involved in recounts. Christopher said vice president's campaign seeks to extend the deadline only as long as it takes to count the votes by hand, perhaps "a few days." Bush's campaign joined the case on behalf of Harris.
Judge Michael McDermott, chairman of Volusia County's canvassing board, was optimistic that its recount work would be done by midday on Tuesday, in which case he said the county would withdraw its suit.
Leon County Circuit Judge Terry Lewis said he will not return a decision in the Volusia case until about 10:30 a.m. Tuesday.
The third legal front opened up late Monday in Broward County.
After a sample hand recount showed little change in three precincts, Broward County's canvassing board opted to forgo a hand recount of the entire county. Gore picked up five votes, and Bush none, in the sample tally of one percent of the precincts in the heavily Democratic district.
The Gore campaign said it would go to court to try to reverse the decision, since a difference of five votes in one percent of the county could mean 500 in the county as a whole.
Florida Agriculture Commissioner Bob Crawford, one of three officials in charge of the state's recount, told CBS News on Monday: "We're doing everything we can to make sure that, at the end of the day, we're going to have a fair election that is credible, that people can have confidence in."
Elsewhere in the Sunshine State:
- Palm Beach County: Election workers in this county will begin hand countin more than 400,000 ballots on Tuesday. They expect that process to take until Sunday - past the Tuesday deadline. More than 19,000 ballots were thrown out here, because voters marked more than one choice for president. Voters have complained that they were confused by the "butterfly" design of the ballot, including some Gore voters who now say they inadvertently punched a hole next to Reform Party candidate Pat Buchanan's name. Crawford said if Palm Beach County misses Tuesday's deadline, then the state will use the last machine recount tally.
- Miami-Dade County: The county canvassing board meets Tuesday to decide whether to conduct a manual recount of votes requested by Democrats.
With the Sunshine State still in dispute, Bush has won 29 states for a total of 246 electoral votes. Gore - who added Oregon to his victory column, but lost New Mexico to "too close too call" status on Friday - has won 19 states, plus the District of Columbia, for a total of 262. To win the White House, 270 electoral votes are needed.
Finally, Bush advisers said on Monday that their campaign may seek recounts in some GOP-leaning Florida counties and in states where Gore won narrowly, such as Iowa and Wisconsin. Republicans in Wisconsin set up a toll-free phone number for election fraud complaints that has received hundreds of calls already.