Internal polling by the Democratic Senatorial Campaign Committee painted a less rosy picture, but Mr. Schumer went all out in pursuit of Mr. O’Rourke, even dispatching a close ally, Randi Weingarten, the president of the American Federation of Teachers, to El Paso. Ms. Weingarten had a long conversation with Mr. O’Rourke and his wife about the seat, but the couple pretty much ruled out a Senate candidacy, according to people briefed on the exchange.
In North Carolina, Democratic leaders have thus far been unable to sell a Senate run to the state’s attorney general, Josh Stein, who is Mr. Schumer’s top pick to challenge the incumbent, Senator Thom Tillis, a freshman. Mr. Stein would have the fund-raising prowess to compete in a race where expenditures by the candidates are likely to exceed $100 million.
Mr. Hickenlooper, a former two-term Colorado governor with a centrist bent, would seem perfect to challenge Senator Cory Gardner, who might be the most endangered Republican up for re-election next year, in a state that voted for Hillary Clinton in 2016 and for Barack Obama in 2008 and 2012.
But Mr. Hickenlooper, who is expected to announce his decision on a presidential run next week in Denver, has already turned down repeated entreaties by the Schumer and Cortez Masto team. They have enlisted Senator Michael Bennet, Democrat of Colorado, to keep pressuring Mr. Hickenlooper to lower his sights to a more realistic level.
Likewise, Mr. Tester and other high-profile Democrats of Montana, including Jim Messina, Mr. Obama’s 2012 campaign manager, have been prodding Mr. Bullock to reconsider.
But the Senate is a tough sell for governors, who find it hard to go from running states to running legislative errands as freshmen, and it is an even tougher sell for Westerners who would have to endure long round-trip flights to Washington.
Operatives close to Mr. Schumer and Ms. Cortez Masto view Mr. Hickenlooper as a soft “no” — in part because of Mr. Gardner’s vulnerability. That is exceeded only by Senator Doug Jones, the Democrat who triumphed in a special election in Alabama only after his opponent, Roy S. Moore, was accused of sexually assaulting teenage girls, according to recent polling.