This much is clear from the events of the last two days: Sen. Ted Cruz (R-Tex.) wants to put questions about his citizenship and eligibility to run for president behind him, as evidenced by the release of his birth certificate and promise to renounce his Canadian citizenship.

Combined with the fact that Cruz has made two trips to Iowa this year (with a third slated for October) and is headed to New Hampshire on Friday, and the question of what it would mean for 2016 if Cruz runs for president is worth asking.

"I don't underestimate Cruz," veteran Republican strategist Ed Rogers said generally of the senator. "Some of his efforts have made a lot of party regulars in Washington wince but he has done nothing but make himself stronger in the party nationally since he entered the Senate."

A lot will ultimately depend on what the complete roster of major candidates looks like come 2016. But no matter who runs, it's pretty safe to say that Cruz would be at the rightward end of the field. He is a strict conservative who has shown an unwillingness to move toward the middle on a host of issues, putting him to the right, on some fronts, of even Sens. Marco Rubio (R-Fla.) and Rand Paul (R-Ky.), two other senators being mentioned as possible 2016 candidate. (Consider that Cruz was one of only three senators who voted against the noncontroversial nomination of John Kerry to be secretary of state.)

In other words, Cruz's presence would make the field more conservative, and force other candidates to respond to attacks on their right. On immigration, for example, Cruz did not support the Senate plan championed by Rubio. On defunding Obamacare, Rep. Paul Ryan (R-Wis.), another potential presidential contender, doesn't endorse Cruz's willingness to shut down the government

Of course, Cruz would face some pretty big challenges, too. The biggest issue he would have to confront off the bat is the question of electability. What's good for conservative confabs in Iowa is not always best for the general election.

Even within the structure of the GOP primary, Cruz's fiery conservative rhetoric wouldn't play well everywhere. His politics are not a natural fit for the more independent/moderate leanings of say, the New Hampshire electorate. And while he has an enthusiastic national grassroots base of supporters and donors, competing seriously on national stage would require him to make inroads with influential donors his potential competition has been courting for years. Many of those donors hold pragmatic political views and some will inevitably be concerned about Cruz's electablity.

Think of Cruz as a variable to watch in the 2016 picture. It's truly an open question of whether or not he will run. Others like New Jersey Gov. Chris Christie, Paul, and Rubio appear to be setting the stage for a campaign more vigorously, and have been doing so for a longer amount of time. (Remember, Cruz wasn't even a senator until this year.)

But losing sight of Cruz in the 2016 picture would be a mistake. Because if he does run, he is poised to leave a footprint.