(CBS News) -- With the parties' conventions over and Election Day just weeks away, President Barack Obama has a three-point edge over Republican Mitt Romney among likely voters nationwide in the latest CBS News/New York Times poll.
Forty-nine percent of likely voters said they'll vote for Mr. Obama, 46 percent said Romney and 4 percent said they're undecided in the poll conducted from Sept. 8-12.
This is the first national poll in which CBS News and the New York Times have measured the presidential race among likely voters. The measure for likely voters takes into account voters' reported intent to vote, voting history and other factors that historically affect an individual's decision to vote.
President Obama has a wider lead over Romney among the broader group of registered voters nationwide. 51 percent say they'll vote for Mr. Obama (the first time he is above the 50 percent mark), while 43 percent choose Romney. Heading into the parties' conventions, the President and Romney were neck and neck among registered voters.
There is some room for movement in the presidential race - but not very much. Eighty-six percent of likely voters who back a candidate say their minds are made up, while just 13 percent say it's too early and their minds could still change. Similar percentages of Obama and Romney voters could change their minds.
Enthusiasm compared to past elections
One of the goals of conventions is for political parties to rally their base of support, and it appears the Democrats have made progress on this front. 43 percent of Democrats now say they are more enthusiastic about voting compared to past elections; up from just 27 percent in July. Republicans remain more enthusiastic than Democrats about voting but their enthusiasm level hasn't increased much from two months ago.
Referendum on the president?
One question that is often asked when an incumbent president is running for re-election is whether the country and voters are better off than they were before he took office. Nearly half of voters say their families are about the same - but the rest are divided, with 26 percent better off and 28 percent worse off.
When it comes to the country overall, just a quarter say it is about the same as four years ago. 36 percent say things in the U.S. are better, and 39 percent say things are worse.
Results are highly partisan: 77 percent of Republicans say the country is worse off, while 66 percent of Democrats say the country is better off.
Who's supporting who?
Each candidate is getting the support of nine in 10 of their party stalwarts, while independents are breaking for Romney. Romney beats Mr. Obama among likely voters age 65 and over, but the President leads among younger voters and enjoys his largest lead among voters under age 30.
The gender gap continues. The president leads among likely women voters by double digits, 53-41 percent, but Romney holds a lead among men, 52-44 percent.
The race is close among white college graduates - Romney leads 50-47 percent. However, Romney has a much larger lead among white voters without a college degree, 57-37 percent. The President does better with voters with lower household incomes, 58-37 percent, while Romney leads among wealthier voters, 57-41 percent.
This poll was conducted by telephone from September 8-12, 2012 among 1,301 adults nationwide, including 1,170 registered voters. The sample size for likely voters is 1,162. Not all likely voters are assigned the same probability of voting. Phone numbers were dialed from samples of both standard land-line and cell phones. The error due to sampling for results based on the entire sample, the sample of registered voters, and the sample of likely voters could be plus or minus three percentage points. The error for subgroups may be higher. Percentages may not add to 100% due to rounding. This poll release conforms to the Standards of Disclosure of the National Council on Public Polls.