Correction: The article about congressional primary races incorrectly said that four House incumbents had been defeated by challengers from their own parties up to that point. The number was three; after Tuesday’s primaries, it is now four. This version has been corrected.

On the verge of completing his brush-back of the tea party, Sen. Orrin G. Hatch (R-Utah) enters Tuesday’s primary a heavy favorite to win the GOP nomination for a seventh term, virtually assuring him the chance to become the longest-serving Republican in Senate history.

Once considered a top target by conservative activists for his past bipartisan deal-making, Hatch waged an intricate campaign to appeal to his state’s conservative-leaning voters and aggressively worked to place his supporters at a GOP convention in the spring that put him in the driver’s seat for the runoff primary against an underfunded former state senator.

With polls showing a healthy lead, Hatch has also continued to leverage his close relationship with GOP presidential candidate Mitt Romney, a fellow Mormon who is revered by Utah’s Republican voters for his oversight of the 2002 Winter Olympics. Romney has cut ads on behalf of Hatch, an early supporter of Romney’s 2008 and 2012 presidential bids.

In the days leading up to Tuesday’s vote, the senator’s campaign sent likely GOP voters a mailer with an image of the presumptive presidential nominee and Hatch walking on an airport tarmac, touting Hatch’s experience and, without mentioning it, the possibility that he could become chairman of the vaunted Finance Committee.

“It’s Utah’s time to lead,” the literature says. “Re-elect Orrin Hatch.”

Hatch is one of three incumbents facing a challenge for his or her party’s nomination Tuesday, highlighted by a quartet of challengers to 21-term Rep. Charles B. Rangel (D-N.Y.) in a newly drawn House district that is 55 percent Hispanic. [See related story.]

Ten-term Rep. Nydia M. Velázquez (D-N.Y.) faces a trio of challengers in a district that now includes parts of three New York boroughs, with her opponents coming from each corner of the local Democratic base: a city councilman, a businessman and a Hispanic activist with ties to the Occupy Wall Street movement.

In Colorado, third-term Rep. Doug Lamborn (R), one of the chamber’s most conservative members, faces businessman Robert Blaha, who has spent more than $750,000 of his own money in a campaign portraying Lamborn as an insider taking “perks galore” as a congressman.

With congressional approval ratings mired in the teens for the past year, four House incumbents and one senator have fallen to challengers in primaries.

Several other House incumbents have lost primary battles against fellow incumbents after the decennial redistricting process threw some lawmakers together into the same district.

This anti-incumbent sentiment led many political strategists to believe that Hatch was ripe for the taking, particularly because Utah GOP voters had ousted congressional incumbents in 2010 and 2008 through the state’s complicated system of first holding party conventions with just a few thousand voters. But the 36-year veteran worked to implant his supporters into the convention, and he won more than 59 percent of the vote at the GOP event in April.

Tuesday’s statewide primary, on the same day that Utah serves as the last state to give its support to Romney, will probably draw hundreds of thousands of voters, and Hatch’s enormous financial advantage could prove decisive against former state senator Dan Liljenquist.

If Hatch wins and completes another six-year term, his 42-year tenure will eclipse the career of the late Ted Stevens as the longest-serving GOP senator in history.

The late Strom Thurmond (R-S.C.) served longer — more than 47 years in the Senate — but almost a decade of that tenure was as a Democrat before he switched parties in 1964.