Democratic presidential nominee Joe Biden speaks at a get-out-the-vote drive-in rally at Cleveland Burke Lakefront Airport on November 02, 2020 in Cleveland, Ohio.Drew Angerer | Getty ImagesDemocratic presidential nominee Joe Biden holds narrow leads over President Donald Trump in six states the president aims to defend Tuesday in his bid for a second term, according to a new CNBC/Change Research poll.The survey released Monday finds the former vice president holding at least a slim edge in all of Arizona, Florida, Michigan, North Carolina, Pennsylvania and Wisconsin, all of which Trump won in 2016. Even so, it shows a race within striking distance for the president in most of those electoral college prizes.All six swing states: Biden 50%, Trump 46%Arizona: Biden 50%, Trump 47%Florida: Biden 51%, Trump 48%Michigan: Biden 51%, Trump 44%North Carolina: Biden 49%, Trump 47%Pennsylvania: Biden 50%, Trump 46%Wisconsin: Biden 53%, Trump 45%A separate national CNBC/Change Research poll shows Biden leading Trump by a 52% to 42% margin.The swing-state poll surveyed 3,328 people from Thursday to Sunday and has a margin of error of plus or minus 1.7 percentage points. The national survey, taken over the same time frame, has a sample size of 1,880 likely voters with a margin of error of plus or minus 2.26 percentage points.The polls in the final stretch before Election Day show a clear, but by no means insurmountable, advantage for Biden in the race for the White House. While contests in Arizona, Florida, North Carolina and Pennsylvania appear close, Trump has more ground to make up in Michigan and Wisconsin, two long blue states that helped to propel him to the White House in 2016.It is unclear how much any late shifts in voter sentiment will change the presidential race this year. In an election where Americans cast their ballots early or by mail in staggering numbers, 68% of respondents to both the national and swing-state surveys said they had already voted.In Arizona, 85% of respondents said they already voted, while 82% and 81% of likely voters in Florida and North Carolina, respectively, said the same. Meanwhile, 63% and 57% of Wisconsin and Michigan voters, respectively, said they had cast ballots. In Pennsylvania — which could take days to count mail-in votes — only 40% of respondents said they had voted.Meanwhile, the battleground-state poll shows Democrats leading close races for three pivotal Senate seats. The party winning all of the elections in Arizona, Michigan and North Carolina would go a long way toward it gaining control of the Senate. Republicans currently hold a 53-47 majority.In Arizona’s special election, Democratic former astronaut Mark Kelly leads Republican Sen. Martha McSally by a 51% to 47% margin. Michigan’s Democratic Sen. Gary Peters holds a 51% to 46% edge over GOP Army veteran and businessman John James.In North Carolina, Democratic former state Sen. Cal Cunningham leads Republican Sen. Thom Tillis by a 50% to 46% margin. The CNBC/Change Research polls have found a consistent but small lead for Cunningham throughout the race, even after confirmation of the Democrat’s romantic relationship with a woman who is not his wife.The polls suggest Trump’s performance during his first term, particularly in handling the coronavirus pandemic that has led to more than 230,000 American deaths, hampered him in key states. In the six swing states, 46% of likely voters said they approve of how Trump is handling the virus, versus 54% who disapprove.Nationally, only 41% of respondents said they approve of how the president is managing the outbreak, versus 59% who said they disapprove.At the same time, 53% of voters in the battleground states said they prefer Biden and Democrats to handle coronavirus, versus 47% who chose Trump and Republicans. Nationally, 58% said they would choose Biden and his party to manage the outbreak, while 42% picked the president and his party.Trump got better marks on the economy: 51% of respondents in the swing states and 46% nationally said they approved of how he is handling the issue.The economy and coronavirus appeared to be the defining issues for poll respondents in the final stretch before Election Day when voters were asked to name the three most important topics facing the country.In the swing-state survey, 48% chose the economy, jobs and cost of living, while 41% picked Covid-19. The next biggest concern was political corruption, which 34% of voters chose.Nationally, 44% of voters chose Covid-19, followed by the economy, jobs and cost of living at 43% aand political corruption at 31%.The data signal Biden’s lead has a lot to do with the current occupant of the White House. More than half, or 54%, of swing-state Biden voters said they are primarily voting against Trump, while 46% said they are largely voting for the former vice president.The motivation differs among Trump supporters. More than eight-in-10, or 84%, said they are mostly voting for Trump, while 16% answered they are voting against Biden. — Graphics by CNBC’s Nate RattnerSubscribe to CNBC on YouTube.