Sen. Orrin HatchOrrin HatchTrump, GOP set to battle on spending cuts GOP eyes new push to break up California court Overnight Defense: Senate to vote on defense picks Friday | 41 detainees left at Gitmo | North Korea may be prepping missile launch MORE's (R-Utah) reelection campaign is facing significant primary and general-election difficulties, a new poll found Monday.

Hatch would struggle in a primary battle against Rep. Jason ChaffetzJason ChaffetzJuan Williams: Ethics cloud hangs over Trump Chaffetz says he's 'pleased' Clinton is not president shortly after handshake Why Democrats fear a successful inaugural address from Trump MORE (R-Utah), according to a Deseret News/KSL-TV poll, and the longtime Republican senator is tied with a potential general-election foe, Democratic Rep. Jim MathesonJim MathesonNew president, new Congress, new opportunity First black GOP woman in Congress wins reelection Lobbying world MORE (Utah).

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Forty percent of all Utah voters would renominate Hatch as the Republican candidate for Senate, while 41 percent would choose Chaffetz; 19 percent said they did not know.

Among Republican primary voters, Hatch enjoys a slight, 47-44 percent, advantage over Chaffetz, who's said he'll decide whether to challenge Hatch after Labor Day. But that number might not be as important, especially if the Republican nomination is decided by a convention. Conservative activists dominate those state conventions, and that process was what produced veteran Sen. Bob Bennett's (R-Utah) loss in a primary last year.

But one of Hatch's key arguments against Chaffetz — electability — could be undercut by other numbers in the poll, which show Hatch struggling against a top potential challenger, Matheson.

If the election were held today, Hatch and Matheson would be tied at 47 percent among Utahans, the poll found. Chaffetz enjoys a slight advantage over his fellow member of the delegation; Chaffetz would get 46 percent to Matheson's 45.

The poll, conducted June 13-16, has a 5 percent margin of error.