Originally Published: 09 NOV 22 02:01 ET

Updated: 09 NOV 22 14:45 ET

By Jeremy Herb and Tierney Sneed, CNN

(CNN) -- Election workers are tabulating ballots in key states that will determine the balance of power in Congress as well as more than three dozen statehouses. Because of differing laws, some states have tallied nearly all their ballots -- while others may not finish for several days.

Even before the polls had closed Tuesday, former President Donald Trump and his allies were spreading baseless claims of voter fraud, a repeat of Trump's lies about the 2020 election being stolen. Yet, elections officials from coast to coast reported few problems at the polls on Tuesday, saying that the election went smoothly beyond isolated and mostly minor problems.

Many eyes are now on Arizona, where Election Day ballots from the state's most populous county were reported by early Wednesday, with additional results expected to be reported by Wednesday night. Counting is also expected to continue into Wednesday in Nevada.

Both states feature competitive Senate and gubernatorial races -- and have been a hub of conspiracy theories since the 2020 election.

Kari Lake, the Republican candidate for Arizona governor, has already cast doubt on the 2022 vote, raising concerns about "incompetency" in election administration as she claimed in a Tuesday night speech that the "system we have right now does not work." Her opponent, Secretary of State Katie Hobbs -- the state's chief elections official -- called for patience as she decried efforts by Lake and her allies to sow "doubt and confusion throughout this campaign."

Some counting in Maricopa County, Arizona's most populous, was delayed due to ballots that could not be successfully read at polling places Tuesday. Those ballots were deposited in secure boxes and will be read starting Wednesday morning, said Bill Gates, chair of the county board of supervisors. The county had tabulation issues that arose from a printer problem at about 60 vote centers, though Gates said no voters were turned away from the polls for that reason.

But that didn't stop Trump and his allies from baselessly claiming the issue was a sign of voter fraud, while the former president falsely alleged on his social media account that the Arizona election was being stolen "with bad Machines and DELAY."

Republicans filed a lawsuit to try to extend voting hours in the county's polls due to the voting machine problems, alleging there were long delays, but the bid was rejected by a judge who said there was no evidence of voters unable to vote.

Gates said Maricopa County expects that between 95-99% of all ballots would be counted by Friday. He also acknowledged the county could see more legal action.

"Elections have become more litigious over the past few years. I would not be surprised to see lawsuits," Gates said. "If we see those lawsuits, we're certainly staffed up as a county to address those."

Arizona was one of the key states where Trump and his allies spread false claims of voter fraud after the 2020 election -- and his endorsed candidates in the state for governor and secretary of state have touted his lies about the 2020 election. Maricopa County Republicans launched a so-called "audit" in 2021 conducted by a GOP firm that ultimately affirmed Joe Biden's victory in the state.

Efforts at transparency

Elections officials where the tabulation stretches into Wednesday have sought to bring transparency into the process.

Georgia election officials, where the Senate race is undecided, have provided updates on the ballots left to be counted, as the race between Democratic Sen. Raphael Warnock and Republican Herschel Walker faces the potential of going into a run-off.

"With the number of votes out there, there is no telling where that can go and who that is going to favor or not," Deputy Secretary of State Gabriel Sterling said Tuesday evening, while signaling that there might not be "full clarity" by the time Peach State voters went to bed on Tuesday.

County election officials in Nevada used Twitter to post updates in their processes, with Washoe County -- home to Reno -- seeking to clarify the types of ballots that were included in the tranches of results that were being reported.

Maricopa County's elections department tweeted in the predawn Wednesday hours that its staff was turning to tens of thousands of early voting ballots that were dropped off on Election Day.

Counting ballots for 'a few days'

In Pennsylvania, acting Secretary of State Leigh Chapman said that it would take "a few days" for the state's unofficial election results to be complete, calling on "voters, candidates and the media" to be patient.

"Election officials in all 67 counties are well aware that the eyes of the nation are on the Keystone State tonight," Chapman said Tuesday evening. "And they are counting as fast as they can. But they are also prioritizing accuracy over speed, as they should."

In 2020, Pennsylvania's presidential election wasn't called for several days after Election Day, and it was one of the states where Trump's team aggressively challenged the results. But CNN and other news organizations had already projected early Wednesday that both Democrats John Fetterman and Josh Shapiro had won their respective elections in the state for Senate and governor.

Even as the most-closely watched races have been decided, Pennsylvania is gearing up for a significant legal challenge over the status of several thousand mail-in ballots that were signed with an invalid date. Last week, the state's Supreme Court ruled those ballots should not be counted, but Fetterman's campaign and other groups sued in federal court to count the mail-in votes.

A teleconference in the case over Pennsylvania's inaccurately dated mail ballots is scheduled for Wednesday morning.