WASHINGTON -- New Jersey voters will choose a new Senator Wednesday. But how soon will their choice have an impact in the Senate?

It's not entirely clear, though odds are it will be after the current debt ceiling standoff is resolved.

That means Republicans will likely hold onto one of New Jersey's Senate seats through the latest budget crisis – giving them 46 votes in the Senate, instead of the 45 the GOP had before the late-Sen. Frank Lautenberg died. It also means Democrats will continue to need at least six Republicans to break ranks in order to defeat a filibuster and get a bill through the Senate.

Gov. Christie has until Nov. 13 to certify the results of the special Senate election, though he doesn't expect to take that long.

"The winner of (Wednesday's) election will be sworn in as quickly as possible after the results have been verified and certified. We fully anticipate this to happen before the Nov. 5th election day," said a statement from Gov. Christie's office.

That gives us a date of the latest the new Senator will formally join the chamber, though it might happen faster.

But assuming it takes more than a day or two, and with the debt ceiling deadline expected to hit Thursday, odds are a deal in Congress is cut and voted on before either Democrat Cory Booker or Republican Steve Lonegan is sworn in. (Unless Congress really, really, really goes over the edge.)

Booker is favored to win. If he does, Democrats would have 55 Senate votes. If Lonegan wins, it would be a devastating loss for Democrats who would lose control of what has been a safely blue seat for decades.

Once results are certified, Senate Majority Leader Harry Reid (D., Nev.) would schedule a swearing in. The new senator will replace Republican Jeff Chiesa, who Christie appointed to temporarily replace Lautenberg.

While we're on dates: the original e-mail from Christie's office referred to "Tuesday's election" – probably because that's when elections are generally held. The Republican National Committee made a similar mistake in a tweet Monday urging people to vote (it was quickly corrected).

And many people here in Washington – smart people who make their livings working in and around politics – have asked me about how voting is going in New Jersey today, even though the votes are tomorrow. It all illustrates the challenges both candidates are likely to face in getting people to the polls on a mid-October Wednesday.

You can follow Tamari on Twitter or email him at jtamari@phillynews.com.