Republicans at both ends of Pennsylvania Avenue are looking at their party’s April 27 Senate primary in Pennsylvania with interest. And both the White House and Senate GOP appear to be taking some part in what is going on in a state that may be pivotal to the party’s hopes in 2004.

When it became clear that he was not going to challenge incumbent Sen. Arlen Specter for the state party’s endorsement at this past weekend’s state GOP convention, Rep. Pat Toomey took a pass on attending the event.

The endorsement was seen as critical to the Toomey getting a leg up on Specter, because the official endorsement ensures that a candidate will be given prominent roles in local Republican functions, fundraisers, and so on.

Now Specter has that endorsement, and Toomey faces an election season where he truly will be running as an outsider looking in.

Toomey’s campaign took another hit on Friday, when the White House demanded that the candidate stop using pictures of President Bush in his advertising. The demand shouldn’t have come as much of a surprise, since the White House has already endorsed Specter for the spring primary, and Vice President Dick Cheney has already appeared on Specter’s behalf at in-state fundraisers.

But while the White House has made its desires clear about keeping Specter in place — and in turn ensuring the likely hold of a Senate seat for Republicans — there are rumblings among Senate Republicans that although they’ll welcome Specter back, they would prefer that he not hold a critical chairmanship. And it appears that the White House is of a like mind on this point.

Some background: Eight years ago Senate Republicans agreed to term limit the chairmanships of committees, which means that after the 2004 elections, Sen. Orrin Hatch is due to step aside as chairman of the Senate Judiciary Committee. Specter is in line due to replace him.

“That can’t happen,” says a staffer for a conservative U.S. Senator. “It would doom the Bush administration’s many judicial nominees currently on hold, and those that may come forward. Specter would not play ball on the more conservative selections. And if there is a Supreme Court nominee, watch out.”

Specter, while keeping a lower than usual profile on the Judiciary Committee of late, is no fan of conservative judges, and has been known to side with Democrats on the committee both publicly and privately.

There is an expectation that should the 2004 election go their party’s way, Republicans might be in a position to get a number of federal judgeships through the Senate. As it stands, Republicans appear to be in line for a net pickup of 3 seats.

As a result, there’s been talk among some Senate Republicans to suspend or end the term limits rule, thereby either extending Hatch’s tenure as chairman, or allowing Senate Majority Leader Sen. Bill Frist to place a potentially more cooperative colleague in the chair.

“The Democrats don’t have a term-limit rule,” says the GOP staffer. “Why should we?”

Another Republican Senate staffer, though, wonders if the White House hasn’t already addressed such concerns about Specter with the Senator himself: “The White House didn’t have to take such an upfront position on the Pennsylvania race. Perhaps Specter has already cut a deal. Something like, you back me, and I’ll back you when nominees come forward down the line.”