We wrote in the Morning Fix on Friday about the very real possibility that the 2012 battle for the Senate winds up a draw.

With six seats listed as "toss-ups" in the latest Fix rankings, a split of those seats would lead to the exact same 53-to-47 Democratic majority that we have today. And for a Republican Party that had designs on regaining the majority, that would certainly be a disappointment.

But with 11 days to go, Republicans also continue to have a very real shot at winning that majority. And that's because they have something that Democrats don't: Lots of opportunity.

While the map hasn't exactly trended in the GOP's favor in recent months when it comes to the top races (Indiana, Massachusetts and Missouri, in particular), Republicans continue to have plausible opportunities to win in a huge amount of seats that we currently rate as "lean Democratic."

Recent polls have shown GOP candidates within striking distance -- though still trailing -- in a bunch of "lean Democratic" states: Connecticut, Florida, Maine, Massachusetts, Missouri, Ohio and Pennsylvania.

Republicans can still get to a 50-50 tie in the Senate by winning all six "toss-up" races (in which case the vice president would cast tie-breaking votes), but the viable likely path to a majority for the GOP is to move some of those "lean Democratic" seats into the "toss-up" category and pull an upset against Sen. Bob Casey (D-Pa.) or Sen. Sherrod Brown (D-Ohio).

The good news for Republicans is that there are a bunch of states where they could make that happen.

But if they can't put those seats in play over the next 11 days, the majority math is very tough.

Below, we look at the 10 seats that are most likely to change control on Nov. 6, with No. 1 being the most likely and No. 10 being the least likely. 

To the line!

Off the line: Connecticut

10. Arizona (Republican-controlled): Democrat Richard Carmona deserves credit for staying in the mix until the end in this red state. The former U.S. surgeon general's centrist credentials have propelled him to within a point of Rep. Jeff Flake (R), according to the Real Clear Politics average of polls in the race. The question is whether a rough recent ad from Flake alleging the Democrat has issues with anger and women, and an unadvised quip by Carmona about Candy Crowley will damage the Democrat's standing among women. This race leapfrogs Connecticut, with recent polls suggesting Republican Linda McMahon has lost some traction in that race. (Previous ranking: N/A)

9. Nevada (R): What looked to be a pretty pure toss-up at the start of the cycle is looking a little like appointed Sen. Dean Heller’s (R) race to lose. Every recent independent nonpartisan poll has shown Heller leading by at least a few points, though hardly out of the danger zone. And with Nevada looking like it tilts toward President Obama, Heller will need plenty of crossover votes to win over Rep. Shelley Berkley (D).. (Previous ranking: 8)

8. Virginia (Democratic-controlled): The slim lead that former Democratic National Committee chairman Tim Kaine (D) had opened up over former senator George Allen earlier this fall appears to have disappeared, as Mitt Romney has moved into a statistical dead heat with President Obama at the top of the ballot. Even Republicans acknowledge that Allen’s fate is tied entirely to Romney’s. If Romney wins the state, Allen will likely — though not certainly — win. If Obama carries Virginia, no one on either side of the aisle thinks Allen can get across the finish line first. (Previous ranking: 7)

7. Indiana (R): Richard Mourdock had a very bad week, and he admitted as much. His comments about rape and pregnancy will almost certainly hurt him at least a little bit. And given that he was in an already-tight race with Rep. Joe Donnelly (D-Ind.), that should give Democrats even more hope. The only reason we don’t move this race up further is 1) we haven’t seen a poll since Mourdock’s comments, and 2) Indiana is a Republican and socially conservative state that Mitt Romney is likely to carry by a significant margin. (Previous ranking: 9)

6. Wisconsin (D): The negative ad war here has taken a toll on both candidates in this race. Rep. Tammy Baldwin (D) and former governor Tommy Thompson (R) each had underwater favorability ratings in the most recent Marquette Law School poll. If the race for the White House stays tight in the Badger State, Thompson's crossover appeal will give Republicans confidence heading toward Nov. 6. But Baldwin has given herself a real shot at victory here. (Previous ranking: 6)

5. Montana (D): A judge this week ordered the release of a report on the investigation into a boat crash involving Rep. Denny Rehberg (R-Mont.) in 2009, and Democrats are giddy that they could reap a late game-changer out of it. That aside, the race remains maybe the truest toss-up on the map, with basically every poll within the margin of error and either side leading in about half of them. Sen. Jon Tester (D-Mont.) may be a slight, slight underdog, given the state’s Republican lean. (Previous ranking: 4)

4. North Dakota (D): Give Democrats an enormous amount of credit in this race. There is no one  -- we repeat NO ONE — who thought that the North Dakota open seat would still be competitive 10 days before the election. But former state Attorney General Heidi Heitkamp (D) has shown remarkable staying power, and Rep. Rick Berg (R) has simply been unable to put any real distance between himself and his Democratic rival. While most polling suggests the race is basically tied, we still put a finger (pinky?) on the scale for Berg due to the state’s Republican lean. President Obama will struggle to get the 45 percent he won statewide in 2008, meaning that Heitkamp will have to over-perform the top of the ticket by somewhere between six and 10 points. Doable? Yes. Likely? Not quite. (Previous ranking: 3)

3. Massachusetts (R): Sen. Scott Brown (R) was looking in strong political shape this summer. Then the fall arrived. The Republican's attacks against Elizabeth Warren's (D) claims to Native American heritage have fallen flat, and the Democrat has done well in the three debates, propelling her to a slight lead in the polls. Perhaps most troubling for Brown: A recent poll shows he's lost his edge over Warren when it comes to favorability, which was about the only reason he would win in such a blue state. There's one debate left in this race next week. If Brown doesn't use it to move the needle, it's difficult to see how he pulls ahead here, short of Warren committing a big error. (Previous ranking: 5) 

2. Maine (R): National Republicans made former governor Angus King (I) sweat a bit when they barraged him over the airwaves, narrowing the gap between the front-runner and Republican Charlie Summers. But King got some reinforcements from environmental groups and New York City Mayor Michael Bloomberg, and hasn't relinquished his advantage. (Previous ranking: 2)

1. Nebraska (D): Former senator Bob Kerrey’s (D-Neb.) campaign released a poll this week that showed him trailing state Sen. Deb Fischer (R) by just five points, but national Democrats have yet to run any independent expenditure ads trying to save this seat. Kerrey’s campaign may not believe this is a lost cause, but national Democrats sure seem to. (Previous ranking: 1) 

Sean Sullivan and Chris Cillizza contributed to this report.