First of all, both parties have elected reps who have ended up under criminal investigation and have had to resign or choose not to run for reelection. (The CA Rep who was spending campaign donations on a posh lifestyle and FINALLY chose not to re-run when public pressure got too intense. Dem who had used gov money to pay off women who accused him of sexual harassment. Many more over the years.)  
.
If some of the charges against Omar are true, I'll try to predict a few things, starting with the tax issues.  
First, there will be excuses about the questionable marriage status (if the claims in the linked article are true): "We were married / divorced in religious ceremonies, not in civil ceremonies, blah, blah, blah, and it wasn't properly reported to the city/state/feds." She will try to wiggle out of that conundrum. She'll have to come up with some PROOF and witnesses and try to fix that "mistake" with the authorities.  
.
Tax filings: IF she can fix the marriage status problem legally, she will submit the forms and prove the validity of the "married" status filings. IF NOT ABLE to prove her married status, she will re-file correctly and pay back taxes and penalties and try to put the mess behind her. I think if she "comes clean" with the IRS about the filing status error, if there is one, that she won't be charged. "Although we considered ourselves to be legally married, it was not to the satisfaction of the state authorities. I have corrected ... and I apologize to my constituents for creating this distraction, now resolved."  
.
We have already had this discussion on P&R, too. The IRS can usually collect lots of back taxes without having to refer those cases to their criminal division. It was something like less than 1% or maybe less than 0.2% of all tax returns are referred to the criminal division.  
.
The article says that she was already "caught" on the campaign finance charges and she already made restitution of the $3900 involved. Pull out stock excuses used by every Dem or Rep politician: "I meant to reimburse more quickly." "Part of the trip (99%) was personal, part (1%) was gov related, and I didn't properly allocate the expenses (0% personal; 100% gov)." etc.
.
NOT a good look for Omar. No need for a Special Counsel. Will she "recover" from all of this exposure?  That remains to be seen.  
.
On the Rep side of things, Danielle Stella, a Republican who hopes to challenge Omar in the next election was charged with numerous counts of shoplifting:  
http://nypost.com/2019/07/26/republican-aiming-to-unseat-ilhan-omar-charged-with-felony/
"A Minnesota congressional candidate hoping to unseat Ilhan Omar with promises of being tough on crime faces felony shoplifting charges, according to a report."   "Stella told police that she “remembers arriving at Target to purchase items but nothing else” due to post-traumatic stress disorder, and that she “normally she goes to Target with someone because of anxiety around people,” according to a criminal complaint cited by The Guardian." Anxiety around other people, leading to anti-social behaviors (larceny): that's a good skill for a Congressman to have!

-- Modified on 7/28/2019 1:42:01 AM