But don't make the mistake of thinking his decision means he's conceding a thing, Shays told the Hartford Courant.
"Don't make an assumption because I'm not going to have TV ads that we're not going to win," Shays said. "We're taking our money, whatever we have, and we're going to spend it to talk to 150,000 people. That's how you win a primary."
McMahon, seeking another bite at the political apple, has been on television since May. She waged an unsuccessful Senate bid against Richard Blumenthal in 2010.
Roll Call rates the November race as trending "likely Democratic."
ESPN airwaves get political
Some topics have been called a political football, but here's an instance where the politics may come during football -- in ads at any rate.
Cable sports network ESPN reached a deal for what ultimately results in more political ads appearing on ESPN programs, including professional and college football games, in October and November, The Wall Street Journal reported.
To overcome the issue of most political ads being sold locally while tapping into a revenue stream, ESPN called an audible: It sold a lump of its ad time to a cable operator group that sells time to political campaigns.
ESPN's deal is with NCC Media LLC, an ad-sales venture owned by several big cable operators.
Ed Erhardt, ESPN's president of global customer marketing and sales, says there is "great demand" for ad time from "political parties and the super-PACs," those third-party groups officially known as "independent-expenditure only committees" that can't contribute to candidate campaigns or parties but can engage in unlimited political spending independently of the campaigns.
Dedication to the constituency
Fifteen years since she entered the Capitol as a freshman, Sen. Susan Collins, R-Maine, cast her 5,000th consecutive vote last week -- "nay" on a motion to kill an amendment to a small-business tax relief bill.
"While I recognize that not every vote is a critical vote, at this time when the public's confidence in Congress is so low, casting every single vote sends a strong signal to one's constituents of dedication to the job and to respect for the high privilege that we have been given," Collins told Roll Call just before she cast her milestone vote.
And 5,000 consecutive votes isn't the Senate record, either. That mark belongs to the late Democrat William Proxmire of Wisconsin, who who cast 10,252 votes from April 20, 1966, to Oct. 18, 1988.
Among current senators, fellow Republican Chuck Grassley of Iowa lit up the voting board 6,448 straight times after Thursday's votes.
Collins' pending wedding isn't expected to interfere with her voting, either, Roll Call said.
She plans to wed during the August recess.
In the House, which casts many more votes than the Senate, Rep. William Natcher, D-Ky., who served until his death in 1994, holds the record for the most consecutive roll-call votes: 18,401 over 41 years, until an illness broke the streak. Roll Call reported Natcher was wheeled onto the House floor on a hospital gurney to cast one of his final votes.
Bush 41 to miss GOP convention
Patriarch George H.W. Bush won't attend the Republican National Convention in August because of health problems -- marking the first party convention Bush has missed in more than 35 years.
Bush, 88, has been seen confined to a wheelchair because of vascular parkinsonism, a condition that prevents him from traveling from his home in Kennebunkport, Maine.
"President and Mrs. Bush are more convinced today than ever that we need to get behind Mitt and Ann Romney to help turn this country around, but sadly the situation around President Bush's mobility will prevent them from attending the Tampa convention," Bush spokesman Jim McGrath told The Hill early last week.
The elder President Bush has been on the convention floor every four years since 1980, when he was nominated for vice president.
Jeb Bush, the former Florida governor, will attend the GOP gathering in Tampa, officials said, but details of his role haven't been finalized.
The Hill said it wasn't clear whether former President George W. Bush will make an appearance or a speech.